schur complements of bezoutians and the inversion of block hankel and block toeplitz matrices abstract we derive a closed inversion formula for an np np square block hankel matrix hn 1 wi j with entries wi from the ring of the p p matrices over a field the representation of h 1n 1 relies upon a strong structure preserving property of the schur complements of the nonsingular leading principal submatrices of a certain generalized bezoutian of matrix polynomials these polynomials may be determined by computing iteratively the schur complements of the nonsingular leading principal submatrices of hn 1 in an augmented block hankel matrix h which is a bezoutian matrix up to multiplication by proper reverse matrices since the special structure of the bezoutian matrix is preserved at any step of the computation such method can be efficiently implemented at an overall computational cost of o p3n2 operations in the average case and o p3n3 operations in the worst case in the normal case a suitable modification which uses both divide and conquer strategies and fast polynomial arithmetic reaches the bound of o p3n log2 n arithmetical operations

bifurcations of corank greater than two abstract we study the solution branches of stable and unstable bifurcations in certain three dimensional semilinear elliptic eigenvalue problems with dirichlet boundary conditions numerically by the continuation methods recent fast linear solvers for large sparse continuation problems are briefly reviewed sample numerical results on corank 3 bifurcation points with computer graphic output are reported

on a shallow water model with the coriolis effect abstract in the present study an asymptotic model for wave propagation in shallow water with the effect of the coriolis force is derived from the governing equation in two dimensional flows the transport equation theory is then applied to investigate the local well posedness and wave breaking phenomena for this model the nonexistence of the camassa holm type peaked solution and classification of various traveling wave solutions to the new system are also established moreover it is shown that all the symmetric waves to this model are traveling waves

on the partial realization problem abstract in this paper we take a unified approach to the partial realization problem in which we seek to incorporate ideas from numerical linear algebra most of which were originally developed in other contexts we approach the partial realization problem from several different angles and explore the connections to such topics as factoriza tion of hankel matrices block tridiagonalization generalizations of the lanczos process for biorthogonalization the euclidean algorithm and the principal part con tinued fractions of arne magnus the pade table and the berlekamp masseyalgo rithm in this way we are able to clarify some previous results by rissanen kalman and others and place them in a broader context this leads to several results and concepts which we think are new our analysis is restricted to the scalar case but some definitions and formulations have been rigged to facilitate an extension to the matrix case

existence of a generalized solitary wave solution for water with positive bond number less than 13 abstract the objective of this paper is to give a rigorous answer to the question whether there exists a generalized solitary wave of elevation on water when the nondimensional surface tension coefficient the so called bond number is positive but less than 1 3 and the froude number is near 1 but greater than 1 the main difficulties to overcome are the small amplitude oscillations at infinity and the choice of appropriate banach spaces for the solution of the problem it is shown that an asymptotic expansion developed for this problem indeed yields an approximate solitary wave solution to the exact equations

delay dependent robust stability criteria for uncertain systems with interval time varying delay this paper proposes an approach for the robust stability of uncertain systems with interval time varying delay the key features of the approach include the introduction of uncorrelated augmented matrix items into the lyapunov functional and the use of a tighter bounding technology unlike existing methodologies the proposed approach involves neither free weighting matrices nor any model transformation it can however lead to much less conservative stability criteria than the existing ones for the systems under consideration numerical examples show that the proposed criteria improve the existing results significantly with much less computational effort

conditioning of the steady state semiconductor device problem when solving numerically the steady state semiconductor device problem using appropriate discretizations extremely large condition numbers are often encountered for the linearized discrete device problem these condition numbers are so large that if they represented a sharp bound on the amplification of input errors or even of roundoff errors then the obtained numerical solution would be meaningless as it turns out one major reason for these large numbers is due to poor row and column scaling which is essentially harmless and or can be fixed but another reason could be an ill conditioned device which yields a true loss of significant digits in the numerical calculation in this paper we carry out a conditioning analysis for the steady state device problem we consider various quasilinearizations as well as gummel type iterations and obtain stability bounds which may indeed allow ill conditioning in general these bounds are exponential in the potential variation and are sharp e g for a thyristor but for devices where each smooth subdomain has an ohmic contact e g a pn diode moderate bounds guaranteeing well conditioning are obtained moreover the analysis suggests how various row and column scalings should be applied in order for the measured condition numbers to correspond more realistically to the true loss of significant digits in the calculations

a new iterative method for solving complex symmetric linear systems based on implementation of the quasi minimal residual qmr and biconjugate a orthogonal residual bicor method a new krylov subspace method is presented for solving complex symmetric linear systems the new method can be combined with arbitrary symmetric preconditioners the preconditioned modified hermitian and skew hermitian splitting pmhss preconditioner is used to accelerate the convergence rate of this method numerical experiments indicate that the proposed method and its preconditioned version are efficient and robust in comparison with other krylov subspace methods

local well posedness and wave breaking results for periodic solutions of a shallow water equation for waves of moderate amplitude abstract we study the local well posedness of a periodic nonlinear equation for surface waves of moderate amplitude in shallow water we use an approach proposed by kato which is based on semigroup theory for quasi linear equations we also show that singularities for the model equation can occur only in the form of wave breaking in particular surging breakers

an implementation of the qmr method based on coupled two term recurrences recently we proposed a new krylov subspace iteration the quasi minimal residual algorithm qmr 1 for solving general nonsingular non hermitian systems of linear equations ax b 1

an implementation of the look ahead lanczos algorithm for non hermitian matrices the nonsymmetric lanczos method can be used to compute eigenvalues of large sparse non hermitian matrices or to solve large sparse non hermitian linear systems however the original lanczos algorithm is susceptible to possible breakdowns and potential instabilities an implementation of a look ahead version of the lanczos algorithm is presented that except for the very special situation of an incurable breakdown overcomes these problems by skipping over those steps in which a breakdown or near breakdown would occur in the standard process the proposed algorithm can handle look ahead steps of any length and requires the same number of matrix vector products and inner products as the standard lanczos process without look ahead

preconditioned iterative methods for sparse linear algebra problems arising in circuit simulation the dc operating point of a circuit may be computed by tracking the zero curve of an associated artificial parameter homotopy homotopy algorithms exist that are globally convergent with probability one for the dc operating point problem these algorithms require computing the one dimensional kernel of the jacobian matrix of the homotopy mapping at each step along the zero curve and hence the solution of a linear system of equations at each step these linear systems are typically large highly sparse non symmetric and indefinite several iterative methods which are applicable to such problems including craig s method gmres k bicgstab qmr kacz and lsqr are applied to a suite of test problems derived from simulations of actual bipolar circuits preconditioning techniques considered include incomplete lu factorization ilu sparse submatrix ilu and ilu allowing restricted fill in bands or blocks timings and convergence statistics are given for each iterative method and preconditioner

computation of matrix valued formally orthogonal polynomials and applications we present a computational procedure for generating formally orthogonal polynomials associated with a given bilinear hankel form with rectangular matrix valued moments our approach covers the most general case of moments of any size and is not restricted to square moments moreover our algorithm has a built in deflation procedure to handle linearly dependent or almost linearly dependent columns and rows of the block hankel matrix associated with the bilinear form possible singular or close to singular leading principal submatrices of the deflated block hankel matrix are avoided by means of look ahead techniques applications of the computational procedure to eigenvalue computations reduced order modeling the solution of multiple linear systems and the fast solution of block hankel systems are also briefly described

global conservative solutions of the camassa holm equation this paper develops a new approach in the analysis of the camassa holm equation by introducing a new set of independent and dependent variables the equation is transformed into a semilinear system whose solutions are obtained as fixed points of a contractive transformation these new variables resolve all singularities due to possible wave breaking returning to the original variables we obtain a semigroup of global solutions depending continuously on the initial data our solutions are conservative in the sense that the total energy equals a constant for almost every time

the lanczos algorithm and hankel matrix factorization abstract we explore the connections between the lanczos algorithm for matrix tridiagonalization and two fast algorithms for hankel matrix factorization we show how the asymmetric lanczos process is related to the berlekamp massey algorithm and how the symmetrized lanczos process is related to the phillips algorithm we also discuss conditions under which the analysis of phillips applies

further optimized look ahead recurrences for adjacent rows in the pade table and toeplitz matrix factorizations abstract in a recent paper we introduced a new look ahead algorithm for recursively computing pade approximants this algorithm generates a subsequence of the pade approximants on two adjacent rows defined by fixed numerator degree of the pade table its two basic versions reduce to the classical levinson and schur algorithms if no look ahead is required in this paper we show that the computational overhead of the look ahead steps in the o n2 versions of the look ahead levinson and the look ahead schur type algorithm can be further reduced if the algorithms are used to solve toeplitz systems of equations tx b then the corresponding block ldu decompositions of t 1 or t respectively can be found with less computational effort than with any other look ahead algorithm available today

an improved digital redesign for sampled data fuzzy control systems this paper proposes an improved digital redesign dr technique for sampled data fuzzy controllers in nonlinear systems based on a takagisugeno ts fuzzy model to improve the performance of the dr technique two methodologies are used a state matching error cost function and a continuous time fuzzy lyapunov function using these two methodologies a novel dr technique is proposed to guarantee both the stability and state matching conditions of the sampled data fuzzy control system further the proposed dr technique is represented as an optimal problem using the linear matrix inequality lmi format finally some simulation examples are provided to verify the effectiveness of the proposed technique in comparison with previous techniques

global existence for small data of the viscous green naghdi type equations abstract we consider the cauchy problem for the green naghdi equations with viscosity for small initial data it is well known that adding a second order dissipative term to a hyperbolic system leads to the existence of global smooth solutions once the hyperbolic system is symmetrizable and the so called kawashima shizuta condition is satisfied in a previous work we have proved that the green naghdi equations can be written in a symmetric form using the associated hamiltonian this system being dispersive in the sense that it involves third order derivatives the symmetric form is based on symmetric differential operators in this paper we use this structure for an appropriate change of variable to prove that adding viscosity effects through a second order term leads to global existence of smooth solutions for small data we also deduce that constant solutions are asymptotically stable

well posedness of a highly nonlinear shallow water equation on the circle abstract we present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation furthermore we establish a novel result concerning the local well posedness of the corresponding cauchy problem for space periodic solutions with initial data from the sobolev space h s on the circle for s 3 2

orbital stability of solitary waves of moderate amplitude in shallow water abstract we study the orbital stability of solitary traveling wave solutions of an equation for surface water waves of moderate amplitude in the shallow water regime our approach is based on a method proposed by grillakis shatah and strauss 1987 1 and relies on a reformulation of the evolution equation in hamiltonian form we deduce stability of solitary waves by proving the convexity of a scalar function which is based on two nonlinear functionals that are preserved under the flow

a fuzzy lyapunov krasovskii functional approach to sampled data output feedback stabilization of polynomial fuzzy systems this paper presents an output feedback exponential stabilization condition of sampled data polynomial fuzzy control systems under variable sampling rates compared with previous work the proposed method is less conservative because of the newly developed time dependent fuzzy lyapunov krasovskii functional that is based on the conventional fuzzy lyapunov function moreover the controller is allowed to contain polynomial gain matrices thereby improving the control performance and design flexibility this is realized by assuming the difference between the continuous and discrete time state vectors as time varying norm bounded uncertainties which are manipulated using a robust control technique a new sufficient condition is introduced to cast the stability condition containing the integral term as the sum of square conditions finally the effectiveness of the proposed method is validated by simulations

network based output tracking control for t s fuzzy systems using an event triggered communication scheme this paper is concerned with network based output tracking control for a t s fuzzy system an event triggered communication scheme under which the threshold depends on the latest successfully transmitted sampled data is introduced to reduce network resource utilization taking the event triggered communication scheme and the asynchronous operation between the fuzzy system and the fuzzy controller the resulting system is modeled as an asynchronous threshold error dependent system with an interval time varying delay a new delay dependent criterion for l 2 gain tracking performance of the asynchronous system is derived by applying the deviation bounds of asynchronous normalized membership functions based on this performance criterion some criteria on the existence of the fuzzy tracking controller are established a co design algorithm is presented to obtain the control gains and the event triggering parameters simultaneously an example is given to illustrate the effectiveness of the proposed method

iterative solution of linear systems in the 20th century this paper sketches the main research developments in the area of iterative methods for solving linear systems during the 20th century although iterative methods for solving linear systems nd their origin in the early 19th century work by gauss the eld has seen an explosion of activity spurred by demand due to extraordinary technological advances in engineering and sciences the past ve decades have been particularly rich in new developments ending with the availability of large toolbox of specialized algorithms for solving the very large problems which arise in scientic and industrial computational models as in any other scientic area research in iterative methods has been a journey characterized by a chain of contributions building on each other it is the aim of this paper not only to sketch the most signicant of these contributions during the past century but also to relate them to one another c 2000 elsevier science b v all rights reserved

on a shallow water approximation to the green naghdi equations with the coriolis effect abstract we consider an asymptotic 1d in space rotation camassa holm r ch model which could be used to describe the propagation of long crested shallow water waves in the equatorial ocean regions with allowance for the weak coriolis effect due to the earth s rotation this model equation has similar wave breaking phenomena as the camassa holm equation it is analogous to the rotation green naghdi r gn equations with the weak earth s rotation effect modeling the propagation of wave allowing large amplitude in shallow water we provide here a rigorous justification showing that solutions of the r gn equations tend to associated solution of the r ch model equation in the camassa holm regime with the small amplitude and the larger wavelength furthermore we demonstrate that the r gn model equations are locally well posed in a sobolev space by the refined energy estimates

large time existence for 1d green naghdi equations we consider here the 1d green naghdi equations that are commonly used in coastal oceanography to describe the propagation of large amplitude surface waves we show that the solution of the green naghdi equations can be constructed by a standard picard iterative scheme so that there is no loss of regularity of the solution with respect to the initial condition

nonfragile exponential synchronization of delayed complex dynamical networks with memory sampled data control this paper considers nonfragile exponential synchronization for complex dynamical networks cdns with time varying coupling delay the sampled data feedback control which is assumed to allow norm bounded uncertainty and involves a constant signal transmission delay is constructed for the first time in this paper by constructing a suitable augmented lyapunov function and with the help of introduced integral inequalities and employing the convex combination technique a sufficient condition is developed such that the nonfragile exponential stability of the error system is guaranteed as a result for the case of sampled data control free of norm bound uncertainties some sufficient conditions of sampled data synchronization criteria for the cdns with time varying coupling delay are presented as the formulations are in the framework of linear matrix inequality these conditions can be easily solved and implemented two illustrative examples are presented to demonstrate the effectiveness and merits of the proposed feedback control

well posedness and blow up solutions for an integrable nonlinearly dispersive model wave equation abstract we establish local well posedness in the sobolev space hs with any s 3 2 for an integrable nonlinearly dispersive wave equation arising as a model for shallow water waves known as the camassa holm equation however unlike the more familiar korteweg devries model we demonstrate conditions on the initial data that lead to finite time blow up of certain solutions

adaptive control of a class of slowly time varying plants abstract an adaptive control system of the type considered earlier by the author which is designed to be stable under the assumption that the unknown plant parameters are constant is shown to maintain stability when the plant parameters are slowly time varying

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

large time existence for 3d water waves and asymptotics we rigorously justify in 3d the main asymptotic models used in coastal oceanography including shallow water equations boussinesq systems kadomtsev petviashvili kp approximation green naghdi equations serre approximation and full dispersion model we first introduce a variable nondimensionalized version of the water waves equations which vary from shallow to deep water and which involves four dimensionless parameters using a nonlocal energy adapted to the equations we can prove a well posedness theorem uniformly with respect to all the parameters its validity ranges therefore from shallow to deep water from small to large surface and bottom variations and from fully to weakly transverse waves

lanczos type variants of the cocr method for complex nonsymmetric linear systems motivated by the celebrated extending applications of the well established complex biconjugate gradient cbicg method to deal with large three dimensional electromagnetic scattering problems by pocock and walker m d pocock s p walker the complex bi conjugate gradient solver applied to large electromagnetic scattering problems computational costs and cost scalings ieee trans antennas propagat 45 1997 140 146 three lanczos type variants of the recent conjugate a orthogonal conjugate residual cocr method of sogabe and zhang t sogabe s l zhang a cocr method for solving complex symmetric linear systems j comput appl math 199 2007 297 303 are explored for the solution of complex nonsymmetric linear systems the first two can be respectively considered as mathematically equivalent but numerically improved popularizing versions of the bicr and crs methods for complex systems presented in sogabe s ph d dissertation and the last one is somewhat new and is a stabilized and more smoothly converging variant of the first two in some circumstances the presented algorithms are with the hope of obtaining smoother and hopefully faster convergence behavior in comparison with the cbicg method as well as its two corresponding variants this motivation is demonstrated by numerical experiments performed on some selective matrices borrowed from the university of florida sparse matrix collection by davis

iterative line cubic spline collocation methods for elliptic partial differential equations in several dimensions this paper presents a new class of second and fourth order line cubic spline collocation methods the lcsc methods for multidimensional linear elliptic partial differential equations with no cross derivative terms the lcsc methods approximate the differential operator along lines in each dimension independently and then combine the results into one large linear system expressed in terms of discretization stencils for the operator these methods have nonzero entries only in the coordinate directions the advantage of this approach is that the discretization is much simpler to derive and analyze further iterative methods are easily applied to the resulting linear systems especially on parallel computers the disadvantage is that the resulting linear system is k times larger in k dimensions using the simplicity of the methods iterative schemes are analyzed and formulated in order to solve the resulting lcsc linear systems in the case of helmholtz problems block jacobi extrapolated jacobi ej and

corrigendum to local well posedness and wave breaking results for periodic solutions of a shallow water equation for waves of moderate amplitude nonlinear anal 97 2014 145 154 abstract the local well posedness of a periodic nonlinear equation for surface waves of moderate amplitude in shallow water was studied in duruk mutlubas 2014 where an approach proposed by kato based on semigroup theory for quasi linear equations was used it was also shown that singularities for the model equation can occur only in the form of wave breaking in particular surging breakers in this paper we correct the mistake made in the proof of the main result on local well posedness and give the appropriate assumptions followed by the corresponding results

synchronization of ts fuzzy complex dynamical networks with time varying impulsive delays and stochastic effects in this paper global exponential synchronization of takagi sugeno ts fuzzy complex dynamical networks with multiple time varying delays and stochastic perturbations is studied via delayed impulsive distributed control both impulsive and continuous parts of the fuzzy model have different multiple time varying delays which make the considered model general and practical a novel lemma on exponential stability of impulsive delayed differential equations was established in which the impulsive functions exhibit multiple time varying delays by utilizing the proposed lemma lyapunov functions the stochastic analysis techniques and the kronecker product general criteria ensuring global exponential synchronization in mean square of the addressed ts fuzzy complex networks are obtained moreover the theory of function minimum value is utilized to reduce the conservativeness of the obtained synchronization criteria which also makes them simple and easy to be verified in practical applications results of this paper improve and extend some existing ones numerical simulations including small world network coupled with time delayed lorenz system are given to show the effectiveness of the theoretical results

qmr a quasi minimal residual method for non hermitian linear systems the biconjugate gradient bcg method is the natural generalization of the classical conjugate gradient algorithm for hermitian positive definite matrices to general non hermitian linear systems unfortunately the original bcg algorithm is susceptible to possible breakdowns and numerical instabilities in this paper we present a novel bcg like approach the quasi minimal residual qmr method which overcomes the problems of bcg an implementation of qmr based on a look ahead version of the nonsymmetric lanczos algorithm is proposed it is shown how bcg iterates can be recovered stably from the qmr process some further properties of the qmr approach are given and an error bound is presented finally numerical experiments are reported

stabilization of switched continuous time systems with all modes unstable via dwell time switching stabilization of switched systems composed fully of unstable subsystems is one of the most challenging problems in the field of switched systems in this brief paper a sufficient condition ensuring the asymptotic stability of switched continuous time systems with all modes unstable is proposed the main idea is to exploit the stabilization property of switching behaviors to compensate the state divergence made by unstable modes then by using a discretized lyapunov function approach a computable sufficient condition for switched linear systems is proposed in the framework of dwell time it is shown that the time intervals between two successive switching instants are required to be confined by a pair of upper and lower bounds to guarantee the asymptotic stability based on derived results an algorithm is proposed to compute the stability region of admissible dwell time a numerical example is proposed to illustrate our approach

sampled data h fuzzy filtering for nonlinear systems with missing measurements in this paper a sampled data h fuzzy filtering problem is considered for nonlinear systems with missing measurements the nonlinear sampled data system and missing measurements are assumed to be represented by a takagisugeno ts fuzzy system and an independent identically distributed bernoulli random process respectively based on the fuzzy system the h fuzzy filtering problem is formulated to design the sampled data fuzzy filter by using the exponential mean square stability definition the stability condition with an h performance is guaranteed for the fuzzy system with the sampled data fuzzy filter and its sufficient condition is converted into the linear matrix inequality lmi format finally an example is provided to verify the effectiveness of the proposed fuzzy filtering technique

stable protocol admissible synchronizability for high order singular complex networks with switching topologies abstract stable protocol admissible synchronization analysis and design problems for singular complex networks with both connected switching topologies and jointly connected switching topologies are investigated firstly a singular observer type synchronization protocol is introduced where the errors of protocol states among neighboring agents are applied to make complex networks satisfy a specific separation principle which can simplify synchronization analysis and design problems then by the orthonormal projection operators between the synchronization subspace and the complement synchronization subspace stable protocol admissible synchronization problems are transformed into admissible ones of multiple subsystems with lower dimensions and an approach is given to determine the synchronization function furthermore stable protocol admissible synchronizability criteria for connected switching topology cases and jointly connected switching topology cases are proposed respectively finally two numerical examples are given to demonstrate the effectiveness of theoretical results

a flexible inner outer preconditioned gmres algorithm a variant of the gmres algorithm is presented that allows changes in the preconditioning at every step there are many possible applications of the new algorithm some of which are briefly discussed in particular a result of the flexibility of the new variant is that any iterative method can be used as a preconditioner for example the standard gmres algorithm itself can be used as a preconditioner as can cgnr or cgne the conjugate gradient method applied to the normal equations however the more appealing utilization of the method is in conjunction with relaxation techniques possibly multilevel techniques the possibility of changing preconditioners may be exploited to develop efficient iterative methods and to enhance robustness a few numerical experiments are reported to illustrate this fact

rational interpolation via orthogonal polynomials abstract relations between rational interpolants and hankel matrices are investigated a modification of a jacobi like algorithm for rational interpolation proposed in 1 is developed the proposed algorithm eliminates all the auxiliary assumptions required to implement the algorithm of 1 in this way it can be used to construct all existing rational interpolants with the cost of o n 2 arithmetic operations where n 1 is the number of data points

a partial pade via lanczos method for reduced order modeling abstract the classical lanczos process can be used to efficiently generate pade approximants of the transfer function of a given single input single output time invariant linear dynamical system unfortunately in general the resulting reduced order models based on pade approximation do not preserve the stability and possibly passivity of the original linear dynamical system in this paper we describe the use of partial pade approximation for reduced order modeling partial pade approximants have a number of prescribed poles and zeros while the remaining degrees of freedom are used to match the taylor expansion of the original transfer function in as many leading coefficients as possible we present an algorithm for computing partial pade approximants via suitable rank 1 updates of the tridiagonal matrices generated by the lanczos process numerical results for two circuit examples are reported

a hybridized iterative algorithm of the bicorstab and gpbicor methods for solving non hermitian linear systems in this study we derive a new iterative algorithm including its preconditioned version which is a hybridized variant of the biconjugate a orthogonal residual stabilized bicorstab method and the generalized product type solvers based on bicor gpbicor method the proposed method which is named gpbicor m similarly to the gpbicg m method proposed by fujino 2002 can be regarded as an extension of the bicorstab2 method introduced by zhao and huang 2013 inspired by fujino s idea for improving the bicgstab2 method in the established gpbicor m method the parameters computed by the bicorstab method are chosen at successive m iteration steps and afterwards the parameters of the gpbicor method are utilized in the subsequent iteration steps therefore the proposed method can inherit the low computational cost of bicorstab and the attractive convergence of gpbicor extensive numerical convergence results on selected real and complex matrices are shown to assess the performances of the proposed gpbicor m method also against other popular non hermitian krylov subspace methods

a breakdown free variation of the nonsymmetric lanczos algorithms the nonsymmetric lanczos tridiagonalization algorithm is essentially the gram schmidt biorthogonalization method for generating biorthogonal bases of a pair of krylov subspaces it suffers from breakdown and instability when a pivot at some step is zero or nearly zero which is often the result of mismatch of the two krylov subspaces in this paper we propose to modify one of the two krylov subspaces by introducing a new start vector when a pivot is small this new start vector generates another krylov subspace which we add to the old one in an appropriate way so that the gram schmidt method for the modified subspaces yields a recurrence similar to the lanczos algorithm our method enforces the pivots to be above a certain threshold and can handle both exact breakdown and near breakdown in particular we recover lookahead lanczos algorithms and arnoldi s algorithm as two special cases we also discuss theoretical and practical issues concerning the new start procedure and present a convergence analysis as well as some numerical examples

embedding calderon multiplicative preconditioners in multilevel fast multipole algorithms calderon preconditioners have recently been demonstrated to be very successful in stabilizing the electric field integral equation efie for perfect electric conductors at lower frequencies previous authors have shown that by using a dense matrix preconditioner based on the calderon identities the low frequency instability is removed while still maintaining the inherent accuracy of the efie it was also demonstrated that the spectral properties of the caldero n preconditioner are conserved during discretization if the efie operator is discretized with rao wilton glisson expansion functions and the preconditioner with buffa christiansen expansion functions in this article we will show how the calderon multiplicative preconditioner cmp can be combined with fast multipole methods to accelerate the numerical solution leading to an overall complexity of o n logn for the entire iterative solution at low frequencies where the cmp is most useful the traditional multilevel fast multipole algorithm mlfma is unstable and we apply the nondirectional stable plane wave mlfma nspwmlfma that resolves the low frequency breakdown of the mlfma the combined algorithm will be called the cmp nspwmlfma applying the cmp nspwmlfma at open surfaces or very low frequencies leads to certain problems which will be discussed in this article

advanced sampled data synchronization control for complex dynamical networks with coupling time varying delays abstract this study addresses sampled data control in the synchronization problem of complex dynamical networks systems with a coupling time varying delay by constructing the augmented lyapunov krasovskii functionals and using some mathematical techniques a sampled data synchronization criterion is derived as the first result with the framework of linear matrix inequalities based on the first result a sampled data synchronization control method is proposed as the second result finally the effectiveness and superiority of the proposed results will be shown by comparing the maximum sampling period with the established results in two numerical examples

a look ahead lanczos algorithm for unsymmetric matrices abstract the two sided lanczos algorithm is known to suffer from serious breakdowns these occur when the associated moment matrix does not permit triangular factorization we modify the algorithm slightly so that it corresponds to using a 2 x 2 pivot in triangular factorization whenever a 1 x 1 pivot would be dangerous the incidence of breakdown is greatly reduced the price paid is that the tridiagonal matrix produced by the algorithm now has bumps whenever a 2 x 2 pivot is used author

traveling surface waves of moderate amplitude in shallow water we study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the euler equations for inviscid incompressible and homogeneous fluids we obtain solitary waves of elevation and depression including a family of solitary waves with compact support where the amplitude may increase or decrease with respect to the wave speed our approach is based on techniques from dynamical systems and relies on a reformulation of the evolution equation as an autonomous hamiltonian system which facilitates an explicit expression for bounded orbits in the phase plane to establish existence of the corresponding periodic and solitary traveling wave solutions

a shallow water approximation to the full water wave problem we demonstrate that the system of the green naghdi equations as a two directional nonlinearly dispersive wave model is a close approximation to the two dimensional full water wave problem based on the energy estimates and the proof of the well posedness for the green naghdi equations and the water wave problem we compare solutions of the two systems showing that without restrictions on the wave amplitude any two solutions of the two systems remain close at least in some finite time within the shallow water regime provided that their initial data are close in the banach space hs hs 1 for some s as a consequence we show that if the depth of the water compared with the wavelength is sufficiently small the two solutions exist for the same finite time using the uniformly bounded energies defined in the paper 2006 wiley periodicals inc

well posedness of the water waves equations 1 1 presentation of the problem the water waves problem for an ideal liquid consists of describing the motion of the free surface and the evolution of the velocity field of a layer of perfect incompressible irrotational fluid under the influence of gravity in this paper we restrict our attention to the case when the surface is a graph parameterized by a function x where t denotes the time variable and x xi xd rd the horizontal spatial variables the method developed here works equally well for any integer d 1 but the only physically relevant cases are of course d 1 and d 2 the layer of fluid is also delimited from below by a not necessarily flat bottom parameterized by a time independent function b x we denote by q t the fluid domain at time t the incompressibility of the fluids is expressed by 1 1 div v 0 in qu t 0

numerical simulation of gravity waves abstract we present a new spectral method to simulate numerically the waterwave problem in a channel for a fluid of finite or infinite depth it is formulated in terms of the free surface elevation and the velocity potential the numerical method is based on the reduction of this problem to a lower dimensional computation involving surface variables alone to accomplish this we describe the taylor expansion of the dirichlet neumann operator in homogeneous powers of the surface elevation each term is a concatenation of fourier multipliers with powers of and its derivatives and is valid uniformly in wavenumber these are easily calculated using the fast fourier transform the method is illustrated by computing the long time evolution of modulated wave packets and of approximations to the stokes steady wave train by imposing a surface pressure we observe surface steepening in large amplitude evolution and wake and bow wave development for flows with a close to critical froude number finally we give an example of nonlinear evolution of the distribution of energy among normal modes

on the solutions of a model equation for shallow water waves of moderate amplitude abstract this paper is concerned with the cauchy problem of a model equation for shallow water waves of moderate amplitude which was proposed by a constantin and d lannes the hydrodynamical relevance of the camassa holmand degasperis procesi equations arch ration mech anal 192 2009 165 186 first the local well posedness of the model equation is obtained in besov spaces b p r s p r 1 s max 3 2 1 1 p which generalize the sobolev spaces h s by using littlewood paley decomposition and transport equation theory second the local well posedness in critical case with s 3 2 p 2 r 1 is considered moreover with analytic initial data we show that its solutions are analytic in both variables globally in space and locally in time finally persistence properties on strong solutions are also investigated

synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

growth rates for the linearized motion of fluid interfaces away from equilibrium we consider the motion of a two dimensional interface separating an inviscid incompressible irrotational fluid influenced by gravity from a region of zero density we show that under certain conditions the equations of motion linearized about a presumed time dependent solution are wellposed that is linear disturbances have a bounded rate of growth if surface tension is neglected the linear equations are well posed provided the underlying exact motion satisfies a condition on the acceleration of the interface relative to gravity similar to the criterion formulated by g i taylor if surface tension is included the linear equations are well posed without qualifications whether the fluid is above or below the interface an interesting qualitative structure is found for the linear equations a lagrangian approach is used like that of numerical work such as 3 except that the interface is assumed horizontal at infinity certain integral equations which occur involving double layer potentials are shown to be solvable in the present case 1993 john wiley sons inc

a dynamic thick restarted semi refined able algorithm for computing a few selected eigentriplets of large nonsymmetric matrices able method can be used to compute eigentriplets of large scale nonsymmetric matrices however there is no guarantee for the ritz vectors obtained by this method to converge even if the subspace is good enough furthermore for the sake of storage limitation and amount of computations restarting techniques are often needed in order to deal with these problems we propose a dynamic thick restarted semi refined able algorithm sable in which we use semi refined ritz vectors to approximate the desired eigenvectors the relationship between the novel method and the classical one is given theoretical results show that the new method can circumvent the possible danger that exists in the standard one in some degree numerical experiments are made on real world problems and comparisons are drown on the thick restarted able algorithm table and the dynamic thick restarted semi refined able algorithm sable they show that the latter is often more powerful and attractive than its standard counterpart

brief paper h filtering for uncertain stochastic time delay systems with sector bounded nonlinearities in this paper we deal with the robust h filtering problem for a class of uncertain nonlinear time delay stochastic systems the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delays as well as sector bounded nonlinearities we aim at designing a full order filter such that for all admissible uncertainties nonlinearities and time delays the dynamics of the filtering error is guaranteed to be robustly asymptotically stable in the mean square while achieving the prescribed h disturbance rejection attenuation level by using the lyapunov stability theory and ito s differential rule sufficient conditions are first established to ensure the existence of the desired filters which are expressed in the form of a linear matrix inequality lmi then the explicit expression of the desired filter gains is also characterized finally a numerical example is exploited to show the usefulness of the results derived

isobe kakinuma model for water waves as a higher order shallow water approximation abstract we justify rigorously an isobe kakinuma model for water waves as a higher order shallow water approximation in the case of a flat bottom it is known that the full water wave equations are approximated by the shallow water equations with an error of order o 2 where is a small nondimensional parameter defined as the ratio of the mean depth to the typical wavelength the green naghdi equations are known as higher order approximate equations to the water wave equations with an error of order o 4 in this paper we show that the isobe kakinuma model is a much higher order approximation to the water wave equations with an error of order o 6

complex shift and invert strategies for real matrices abstract when using an iterative method for solving a generalized nonsymmetric eigenvalue problem of the form fu mu where f and m are real banded matrices it is often desirable to work with the shifted and inverted operator b f m 1 m in order to enhance the eigenvalue separation and improve efficiency unfortunately the shift is generally complex and so is the matrix b the question then is whether it is possible to avoid complex arithmetic while preserving any advantages of bandedness of the pair f m for the classical problem where m i and f is banded complex arithmetic can be avoided by using double shifts i e by working with the real matrix bb whose bandwidth is double that of f this satisfactory solution extends to the case where m is diagonal as well in the generalized case the answer to the above question is negative in the sense that complex arithmetic can be avoided only at the expense of losing the advantage of bandedness one solution is to factor the shifted matrix f m in complex arithmetic but employ real arithmetic subsequently in the iterative procedure this paper examines several approaches and discusses their respective merits under various circumstances

linear stability of solitary waves of the green naghdi equations we investigate the eigenvalue problem obtained from linearizing the green naghdi equations about solitary wave solutions unlike weakly nonlinear water wave models the physical system considered here has nonlinearity in its highest derivative term this results in more detailed asymptotic analysis of the eigenvalue problem in the presence of a large parameter combining the technique of singular perturbation with the evans function we show that for solitary waves of small amplitude the problem has no eigenvalues of positive real part and the evans function is nonvanishing everywhere except the origin this fact then leads to the linear stability of these solitary waves 2001 john wiley sons inc

on the low regularity solutions and wave breaking for an equation modeling shallow water waves of moderate amplitude abstract in this paper we consider a nonlinear evolution equation which models the propagation of surface waves of moderate amplitude in shallow water regime we first prove the existence of the low regularity solutions for the cauchy problem of this equation then we discuss the initial profiles under which the solutions of this equation blow up in finite time

technical communique improved delay range dependent stability criteria for linear systems with time varying delays this paper is concerned with the stability analysis of linear systems with time varying delays in a given range a new type of augmented lyapunov functional is proposed which contains some triple integral terms in the proposed lyapunov functional the information on the lower bound of the delay is fully exploited some new stability criteria are derived in terms of linear matrix inequalities without introducing any free weighting matrices numerical examples are given to illustrate the effectiveness of the proposed method

on the long wave approximation for the euler poisson system abstract we study the long wave approximation to the euler poisson system for the ion acoustic wave in cold plasma according to the spatial temporal scale and the amplitude of waves we first justify rigorously that in the long wave limit the one way propagating solutions of the euler poisson system are well approximated by the unidirectional solutions of the burgers or kdv equation with responding to the different parameter scales we then demonstrate that the solutions could be convergent to two wave packets in opposite directions where each wave packet involves independently as a solution of the burgers or kdv equation

local stability analysis of continuous time takagi sugeno fuzzy systems a fuzzy lyapunov function approach this paper proposes a strategy to estimate invariant subsets of the domain of attraction da for asymptotically stable zero equilibrium points of continuous time takagi sugeno t s fuzzy systems specifically by using lyapunov s stability theory and the linear matrix inequality lmi technique sufficient conditions for proving the local stability are provided in terms of single parameter minimization problems subject to lmi constraints or eigenvalue problems which are solvable via convex optimizations the fuzzy lyapunov functions flfs expressed by the so called multi dimensional fuzzy summations are employed to characterize invariant subsets of the da as sublevel sets of the flfs to compute a larger inner estimate of the da an iterative lmi algorithm is also developed finally illustrative examples show the efficacy of the approach

a new implementation of the cmrh method for solving dense linear systems the cmrh method h sadok methodes de projections pour les systemes lineaires et non lineaires habilitation thesis university of lille1 lille france 1994 h sadok cmrh a new method for solving nonsymmetric linear systems based on the hessenberg reduction algorithm numer algorithms 20 1999 303 321 is an algorithm for solving nonsymmetric linear systems in which the arnoldi component of gmres is replaced by the hessenberg process which generates krylov basis vectors which are orthogonal to standard unit basis vectors rather than mutually orthogonal the iterate is formed from these vectors by solving a small least squares problem involving a hessenberg matrix like gmres this method requires one matrix vector product per iteration however it can be implemented to require half as much arithmetic work and less storage moreover numerical experiments show that this method performs accurately and reduces the residual about as fast as gmres with this new implementation we show that the cmrh method is the only method with long term recurrence which requires not storing at the same time the entire krylov vectors basis and the original matrix as in the gmres algorithm a comparison with gaussian elimination is provided

a krylov subspace projection method for simultaneous solution of helmholtz problems at multiple frequencies abstract a krylov subspace projection method which provides simultaneous solutions of the helmholtz equation at multiple frequencies in one solution step is presented the projector is obtained with an unsymmetric block lanczos algorithm applied to a transfer function derived from a finite element discretization this approach is equivalent to a matrix valued pade approximation of the transfer function the proposed method is an extension of the formulation presented in j comput acoust 8 2000 223 to unsymmetric systems and allows the treatment of a much wider range of practical problems including near field and fluid structure interaction computations

ml n bicgstabt a ml n bicgstab variant with a transpose the 1980 idr method wesseling and sonneveld 1980 12 plays an important role in the history of krylov subspace methods it started the research of transpose free krylov subspace methods the ml n bicgstab method yeung 2012 is one of such methods in this paper we present a new ml n bicgstab variant that involves a transpose in its implementation comparison of this new algorithm with the existing ml n bicgstab algorithms and some other krylov subspace algorithms will be presented

on the blow up structure for the generalized periodic camassa holm and degasperis procesi equations considered herein are the generalized camassa holm and degasperis procesi equations in the spatially periodic setting the precise blow up scenarios of strong solutions are derived for both of equations several conditions on the initial data guaranteeing the development of singularities in finite time for strong solutions of these two equations are established the exact blow up rates are also determined finally geometric descriptions of these two integrable equations from non stretching invariant curve flows in centro equiaffine geometries pseudo spherical surfaces and affine surfaces are given

new look ahead lanczos type algorithms for linear systems a breakdown due to a division by zero can arise in the algorithms for implementing lanczos method because of the non existence of some formal orthogonal polynomials or because the recurrence relationship used is not appropriate such a breakdown can be avoided by jumping over the polynomials involved this strategy was already used in some algorithms such as the mrz and its variants in this paper we propose new implementations of the recurrence relations of these algorithms which only need the storage of a fixed number of vectors independent of the length of the jump these new algorithms are based on horner s rule and on a different way for computing the coefficients of the recurrence relationships moreover these new algorithms seem to be more stable than the old ones and they provide better numerical results numerical examples and comparisons with other algorithms will be given

a review of formal orthogonality in lanczos based methods krylov subspace methods and their variants are presently the favorite iterative methods for solving a system of linear equations although it is a purely linear algebra problem it can be tackled by the theory of formal orthogonal polynomials this theory helps to understand the origin of the algorithms for the implementation of krylov subspace methods and moreover the use of formal orthogonal polynomials brings a major simplification in the treatment of some numerical problems related to these algorithms this paper reviews this approach in the case of lanczos method and its variants the novelty being the introduction of a preconditioner

reciprocally convex approach to stability of systems with time varying delays whereas the upper bound lemma for matrix cross product introduced by park 1999 and modified by moon park kwon and lee 2001 plays a key role in guiding various delay dependent criteria for delayed systems the jensen inequality has become an alternative as a way of reducing the number of decision variables it directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities resulting in a linear combination of positive functions weighted by the inverses of convex parameters this paper suggests the lower bound lemma for such a combination which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables comparable to those based on the jensen inequality lemma

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

a breakdown free lanczos type algorithm for solving linear systems lanczos type algorithms for solving systems of linear equations have their foundations in the theory of formal orthogonal polynomials and the method of moments which leads to a determinantal formula for their iterates the various lanczos type algorithms mainly differ by the way of computing the coefficients entering into the recurrence formulae if the denominator in the formula for one of these coefficients is zero then a breakdown occurs in the algorithm and it must be stopped such a breakdown is in fact due to the non existence of some orthogonal polynomial in this paper we show how to jump over such a singularity by computing the next existing orthogonal polynomial by the block bordering method the resulting algorithm called mrz is equivalent to the nongeneric biodir algorithm which is a look ahead lanczos type algorithm but our derivation is much simpler

the lanczos biorthogonalization algorithm and other oblique projection methods for solving large unsymmetric systems many powerful methods for solving systems of equations can be regarded as projection methods most of the projection methods known for solving linear systems are orthogonal projection methods but little attention has been given to the class of nonorthogonal or oblique projection methods which is particularly attractive for large nonsymmetric systems the purpose of the paper is to present some methods in the general setting of oblique projection methods and to give some theoretical results some experiments comparing the various algorithms are reported

finite time synchronization of sampled data t s fuzzy complex dynamical networks subject to average dwell time approach abstract the problem of finite time synchronization for takagi sugeno t s fuzzy complex dynamical networks with coupling delays via sampled data control is presented in this paper to change the sampled data control system into a continuous time delayed system an input delay approach is applied based on the lyapunov stability theory a suitable lyapunov krasovskii functional lkf is constructed with the kronecker products furthermore by applying the average dwell time approach a novel sufficient condition is established to ascertain the finite time stabilization of fuzzy complex dynamical networks cdns with switching signals the proposed method is less conservative than conventional approaches since the newly developed time dependent fuzzy lkf is used the proposed sufficient condition can be represented in the form of linear matrix inequalities lmis finally the effectiveness and superiority of the proposed approach is validated through both numerical and practical examples

hybrid state space fuzzy model based controller with dual rate sampling for digital control of chaotic systems we develop a hybrid state space fuzzy model based controller with dual rate sampling for digital control of chaotic systems a takagi sugeno ts fuzzy model is used to model the chaotic dynamic system and the extended parallel distributed compensation technique is proposed and formulated for designing the fuzzy model based controller under stability conditions the optimal regional pole assignment technique is also adopted in the design of the local feedback controllers for the multiple ts linear state space models the proposed design procedure is as follows an equivalent fast rate discrete time state space model of the continuous time system is first constructed by using fuzzy inference systems to obtain the continuous time optimal state feedback gains the constructed discrete time fuzzy system is then converted into a continuous time system the developed optimal continuous time control law is finally converted into an equivalent slow rate digital control law using the proposed intelligent digital redesign method the main contribution of the paper is the development of a systematic and effective framework for fuzzy model based controller design with dual rate sampling for digital control of complex such as chaotic systems the effectiveness and the feasibility of the proposed controller design method is demonstrated through numerical simulations on the chaotic chua circuit

well posedness in sobolev spaces of the full water wave problem in 2 d we consider the motion of the interface of 2 d irrotational incompressible inviscid water wave with air above water and surface tension zero we show that the interface is always not accelerating into the water region normal to itself as rapidly as the normal acceleration of gravity as long as the interface is nonself intersect we therefore obtain the existence and uniqueness of solutions of the full water wave problem locally in time for any initial interface which is nonself intersect including the case that the interface is of multiple heights

the long wave limit for the water wave problem i the case of zero surface tension the korteweg de vries equation boussinesq equation and many other equations can be formally derived as approximate equations for the two dimensional water wave problem in the limit of long waves here we consider the classical problem concerning the validity of these equations for the water wave problem in an infinitely long canal without surface tension we prove that the solutions of the water wave problem in the long wave limit split up into two wave packets one moving to the right and one to the left where each of these wave packets evolves independently as a solution of a korteweg de vries equation our result allows us to describe the nonlinear interaction of solitary waves 2000 john wiley sons inc

a transpose free quasi minimal residual variant of the cors method for solving non hermitian linear systems recently the conjugate a orthogonal residual squared cors method is often competitive and superior to other krylov subspace methods for solving complex non hermitian linear systems from many realistic problems however like the conjugate gradient squared cgs method the cors method often exhibits irregular convergence behavior with wild oscillations in the residual norm to try and remedy this problem we develop a transpose free quasi minimal residual tfqmr variant of the cors method which leads to smooth convergence curves with a convergence rate similar to the cors method we also give convergence results for this new method finally numerical examples are reported to illustrate the effectiveness of the proposed method