adaptive low gain integral control of multivariable well posed linear systems the principle of low gain integral control for finite dimensional systems is well known more recently low gain integral control results have been obtained for classes of infinite dimensional systems in this paper we show that integral control with a simple and natural adaptation of the integrator gain achieves tracking of constant reference signals for every exponentially stable multivariable well posed infinite dimensional linear system whose steady state gain matrix has its spectrum in the open right half plane our results considerably extend improve and simplify previous work by the authors siam j control optim 35 1997 pp 78 116

an adaptive tracking problem with a control input constraint abstract in this paper we consider the problem of controlling an uncertain linear time invariant lti continuous time plant when there is a control input constraint a switching controller is presented which will carry out asymptotic error regulation for constant reference and constant disturbance signals which are compatible with the control input constraint assuming that i the plant is asymptotically stable ii the plant has no transmission zeros at zero and iii the plant has as many inputs as outputs this controller is quite easy to implement especially in the single input single output siso case and is noise tolerant some examples including a model of a three input three output distillation column are included to illustrate the controller behaviour

restarted gmres preconditioned by deflation this paper presents a new preconditioning technique for the restarted gmres algorithm it is based on an invariant subspace approximation which is updated at each cycle numerical examples show that this deflation technique gives a more robust scheme than the restarted algorithm at a low cost of operations and memory

transfer functions of regular linear systems part ii the system operator and the lax phillips semigroup this paper is a sequel to a paper by the second author on regular linear systems 1994 referred to here as part i we introduce the system operator of a well posed linear system which for a finite dimensional system described by x ax bu y cx du would be the s dependent matrix s s a si c b d in the general case s s is an unbounded operator and we show that it can be split into four blocks as in the finite dimensional case but the splitting is not unique the upper row consists of the uniquely determined blocks a si and b as in the finite dimensional case but the lower row is more problematic for weakly regular systems which are introduced and studied here there exists a special splitting of s s where the right lower block is the feedthrough operator of the system using s 0 we give representation theorems which generalize those from part i to well posed linear systems and also to the situation when the initial time is we also introduce the lax phillips semigroup t induced by a well posed linear system which is in fact an alternative representation of a system used in scattering theory our concept of a lax phillips semigroup differs in several respects from the classical one for example by allowing an index r which determines an exponential weight in the input and output spaces this index allows us to characterize the spectrum of a and also the points where s s is not invertible in terms of the spectrum of the generator of for various values of the system is dissipative if and only if with index zero is a contraction semigroup

a parallel element by element solution scheme a parallel element by element scheme is developed for finite element solution of elliptic boundary value problems it is shown that for a broad class of computational grids the solution algorithm is totally parallelizable moreover the conversion of an existing serial ebe code to a parallel code is seen to be quite simple the method is implemented on the alliant fx 8 and sequent balance parallel computers and speedup performance studies are conducted for a representative elliptic pde in two dimensions the present procedure can be applied quite generally to other finite element applications and the associated programs can be modified in a straightforward way to implement the method

a reduced order model based preconditioner for the efficient solution of transient diffusion equations this paper presents a novel class of preconditioners for the iterative solution of the sequence of symmetric positive definite linear systems arising from the numerical discretization of transient parabolic and selfadjoint partial differential equations the preconditioners are obtained by nesting appropriate projections of reduced order models into the classical iteration of the preconditioned conjugate gradient pcg the main idea is to employ the reduced order solver to project the residual associated with the conjugate gradient iterations onto the space spanned by the reduced bases this approach is particularly appealing for transient systems where the full model solution has to be computed at each time step in these cases the natural reduced space is the one generated by full model solutions at previous time steps when increasing the size of the projection space the proposed methodology highly reduces the system conditioning number and the number of pcg iterations at every time step the cost of the application of the preconditioner linearly increases with the size of the projection basis and a trade off must be found to effectively reduce the pcg computational cost the quality and efficiency of the proposed approach is finally tested in the solution of groundwater flow models c 2016 the authors international journal for numerical methods in engineering published by john wiley sons ltd

on adaptive weighted polynomial preconditioning for hermitian positive definite matrices the conjugate gradient algorithm for solving hermitian positive definite linear systems is usually combined with preconditioning in order to speed up convergence in recent years there has been a revival of polynomial preconditioning motivated by the attractive features of the method on modern architectures standard techniques for choosing the preconditioning polynomial are based only on bounds for the extreme eigenvalues here a different approach is proposed that aims at adapting the preconditioner to the eigenvalue distribution of the coefficient matrix the technique is based on the observation that good estimates for the eigenvalue distribution can be derived after only a few steps of the lanczos process this information is then used to construct a weight function for a suitable chebyshev approximation problem the solution of this problem yields the polynomial preconditioner in particular polynomial preconditioners associated with bernstein szego weights are studied results of numerical exper

efficient preconditioner updates for shifted linear systems we present a technique for building effective and low cost preconditioners for sequences of shifted linear systems a alpha i x alpha b where a is symmetric positive definite and alpha 0 this technique updates a preconditioner for a available in the form of an ldl t factorization by modifying only the nonzero entries of the l factor in such a way that the resulting preconditioner mimics the diagonal of the shifted matrix and reproduces its overall behavior this approach is supported by a theoretical analysis as well as by numerical experiments showing that it works efficiently for a broad range of values of alpha

a generalized block fsai preconditioner for nonsymmetric linear systems the efficient solution to nonsymmetric linear systems is still an open issue especially on parallel computers in this paper we generalize to the unsymmetric case the block factorized sparse approximate inverse block fsai preconditioner which has already proved very effective on symmetric positive definite spd problems block fsai is a hybrid approach combining an inner preconditioner with the aim of transforming the system matrix structure to block diagonal with an outer one a block diagonal incomplete or exact factorization intended to improve the conditioning of each block the proposed algorithm is experimented with in a number of large size matrices showing both a good robustness and scalability

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

robust approximate inverse preconditioning for the conjugate gradient method we present a variant of the ainv factorized sparse approximate inverse algorithm which is applicable to any symmetric positive definite matrix the new preconditioner is breakdown free and when used in conjunction with the conjugate gradient method results in a reliable solver for highly ill conditioned linear systems we also investigate an alternative approach to a stable approximate inverse algorithm based on the idea of diagonally compensated reduction of matrix entries the results of numerical tests on challenging linear systems arising from finite element modeling of elasticity and diffusion problems are presented

semigroup properties and the crandall liggett approximation for a class of differential equations with state dependent delays abstract we present an approach for the resolution of a class of differential equations with state dependent delays by the theory of strongly continuous nonlinear semigroups we show that this class determines a strongly continuous semigroup in a closed subset of c 0 1 we characterize the infinitesimal generator of this semigroup through its domain finally an approximation of the crandall liggett type for the semigroup is obtained in a dense subset of c as far as we know this approach is new in the context of state dependent delay equations while it is classical in the case of constant delay differential equations

the state feedback regulator problem for regular linear systems this paper is about the state feedback regulator problem for infinite dimensional linear systems the plant assumed to be an exponentially stable regular linear system is driven by a linear possibly infinite dimensional exosystem via a disturbance signal the exosystem has its spectrum in the closed right half plane and also generates the reference signal for the plant output the regulator problem is to design a controller that while guaranteeing the stability of the closed loop system without the exosystem drives the tracking error to zero a particular version of this problem is the state feedback regulator problem in which the states of the exosystem and the plant are known to the controller under suitable assumptions we show that the latter problem is solvable if and only if a pair of algebraic equations called the regulator equations is solvable we derive conditions in terms of the transfer function of the plant and eigenvalues of the exosystem for the solvability of the regulator equations three examples illustrating the theory are presented

comparison of krylov subspace methods with preconditioning techniques for solving boundary value problems abstract in this paper we made an attempt to establish the usefulness of lanczos solver with preconditioning technique over the preconditioned conjugate gradient cg solvers we have presented here a detail comparative study with respect to convergence speed as well as cpu time by considering appropriate boundary value problems

robust stability of systems with integral control a number of necessary and sufficient conditions are derived which must be satisfied by the plant d c gain matrix of a linear time invariant system in order for an integral controller to exist for which the closed loop system is stable based on these results the robustness of integral control systems is analyzed i e the family of plants is defined which are stable when controlled with the same integral controller conditions for actuator sensor failure tolerance of systems with integral control are also given finally parallels are drawn between the results of this paper and the bifurcation theory of nonlinear systems

necessary and sufficient conditions for the simplification of generalized conjugate gradient algorithms recent papers by faber and manteuffel characterize the cases where orthodir a generalized conjugate gradient algorithm for solving complex non hermitian linear systems can be defined by a short recurrence formula and thus simplified in the present paper similar results are obtained for two other generalized conjugate gradient algorithms namely orthomin and orthores necessary and sufficient conditions on the coefficient matrix a are given so that simplification is possible illustrative examples are given

integral control of linear systems with actuator nonlinearities lower bounds for the maximal regulating gain closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller is known to ensure asymptotic tracking of constant reference signals provided that 1 the steady state gain of the linear part of the plant is positive 2 the positive integrator gain is sufficiently small and 3 the reference value is feasible in a very natural sense here lower bounds are derived for the maximal regulating gain for various special cases including systems with nonovershooting step response and second order systems with a time delay in the input or output the lower bounds are given in terms of open loop frequency step response data and the lipschitz constant of the nonlinearity and are hence readily obtainable

preconditioning techniques for large linear systems a survey this article surveys preconditioning techniques for the iterative solution of large linear systems with a focus on algebraic methods suitable for general sparse matrices covered topics include progress in incomplete factorization methods sparse approximate inverses reorderings parallelization issues and block and multilevel extensions some of the challenges ahead are also discussed an extensive bibliography completes the paper

iterative solution of indefinite symmetric linear systems by methods using orthogonal polynomials over two disjoint intervals in the classical chebyshev algorithm for solving symmetric positive definite linear systems ax b the approximate solution is of the form x k x 0 s k a r 0 where r 0 b ax 0 is the initial residual and s k is a polynomial of degree k 1 which minimizes 1 lambda s k lambda infty where cdot infty is the uniform norm on some interval s containing the spectrum of a but not the origin if a is not positive definite the set s can be taken to be the union of two disjoint intervals a b and c d with b 0 c and a generalization of the chebyshev algorithm based on the minimax polynomial has been considered by several authors in this paper we propose a new technique based upon the least squares polynomial in the set s i e the polynomial t k which minimizes 1 lambda t k lambda w where cdot w is an l 2 norm with respect to a weight function w lambda defined on s with a suitable weight function w lambda the po

functional evolution equations abstract of concern is the functional evolution equation du dt bu f t u t t 0 u 0 s c 1 r 0 x where ut s u t s r 0 s r 0 and x is a real banach space it is shown by the method of lines combined with the crandall pazy theorem that for the initial data u0 in a generalized domain this equation has a limit solution which is lipschitz continuous in t and that this limit solution is a unique strong one if further assumptions on b are imposed and that the zero solution is asymptotically stable an application is given to a class of partial functional differential boundary value problems

brief integral control by variable sampling based on steady state data in this paper we consider integral control algorithms with convergent adaptive sampling for multivariable infinite dimensional systems steady state gain information is used in choosing suitable integrator gains and we also consider robustness with respect to error in measuring the steady state gain

transfer functions of regular linear systems part i characterizations of regularity we recall the main facts about the representation of regular linear systems essentially that they can be described by equations of the form x t ax t bu t y t cx t du t like finite dimensional systems but now a b and c are in general unbounded operators regular linear systems are a subclass of abstract linear systems we define transfer functions of abstract linear systems via a generalization of a theorem of foures and segal we prove a formula for the transfer function of a regular linear system which is similar to the formula in finite dimensions the main result is a simple to state but hard to prove necessary and sufficient condition for an abstract linear system to be regular in terms of its transfer function other conditions equivalent to regularity are also obtained the main result is a consequence of a new tauberian theorem which is of independent interest

high gain adaptive stabilization of multivariable linear systems revisited abstract we consider the class of multi input multi output finite dimensional state space systems of the form x ax bu y cx where the state dimension is unknown the system is minumum phase and it is known that det cb 0 for this class a universal adaptive high gain controller not based on identification or estimation algorithms is presented which ensures exponential decay of the motion of the closed loop system it is shown that the controller is robust with respect to certain nonlinear perturbations

flexible inner outer krylov subspace methods flexible krylov methods refers to a class of methods which accept preconditioning that can change from one step to the next given a krylov subspace method such as cg gmres qmr etc for the solution of a linear system ax b instead of having a fixed preconditioner m and the right preconditioned equation am 1 y b mx y one may have a different matrix say mk at each step in this paper the case where the preconditioner itself is a krylov subspace method is studied there are several papers in the literature where such a situation is presented and numerical examples given a general theory is provided encompassing many of these cases including truncated methods the overall space where the solution is approximated is no longer a krylov subspace but a subspace of a larger krylov space we show how this subspace keeps growing as the outer iteration progresses thus providing a convergence theory for these inner outer methods numerical tests illustrate some important implementation aspects that make the discussed inner outer methods very appealing in practical circumstances

shifted fsai preconditioners for the efficient parallel solution of non linear groundwater flow models summary the present paper investigates the performance of a shifted factorized sparse approximate inverse as a parallel preconditioner for the iterative solution to the linear systems arising in the finite element discretization of non linear groundwater flow models the shift strategy is based on an inexpensive preconditioner update exploiting the structure of the coefficient matrix the proposed algorithm is experimented with in the parallel simulation of a large scale real multi aquifer system characterized by a stochastic distribution of the hydraulic conductivity the numerical results show that the shifted factorized sparse approximate inverse algorithm may yield an overall computational gain up to 300 with respect to the non shifted scheme with an excellent parallel efficiency copyright 2011 john wiley sons ltd

low gain integral control for multi input multioutput linear systems with input nonlinearities we consider the inclusion of a static antiwindup component in a continuous time low gain integral controller in feedback with a multi input multi output stable linear system subject to an input nonlinearity from a class of functions that includes componentwise diagonal saturation we demonstrate that the output of the closed loop system asymptotically tracks every constant reference vector which is feasible in a natural sense provided that the integrator gain is sufficiently small robustness properties of the proposed control scheme are investigated and three examples are discussed in detail

structural optimization based on preconditioned conjugate gradient analysis methods an efficient method for structural optimization is presented instead of classical direct decomposition methods preconditioned conjugate gradient pcg methods in conjunction with two proposed starting vector generation schemes are used to solve the systems of linear equations associated with the finite element analysis and behaviour sensitivity analysis problems these inherently iterative analysis procedures are then used to carry out the analyses needed at the beginning of each stage in an approximation concepts approach to structural optimization this technique has been implemented in a research program and used to solve a collection of minimum weight truss sizing design problems subject to static deflection and stress constraints the effectiveness of the pcg methods of analysis in structural optimization is demonstrated comparison among different preconditioners is made the effect of the proposed starting vector generation schemes is shown the comparative merits of analytical sensitivity analysis and finite difference sensitivity analysis when using pcg methods of analysis are assessed the parallel computation potential of pcg methods is discussed because of the iterative nature of pcg analysis methods and the prospects they offer for parallel computation it is found that pcg analysis methods show promise in the context of structural optimization

approximate inverse preconditioners via sparse sparse iterations the standard incomplete lu ilu preconditioners often fail for general sparse indefinite matrices because they give rise to unstable factors l and u in such cases it may be attractive to approximate the inverse of the matrix directly this paper focuses on approximate inverse preconditioners based on minimizing i am f where am is the preconditioned matrix an iterative descent type method is used to approximate each column of the inverse for this approach to be efficient the iteration must be done in sparse mode i e with sparse matrix by sparse vector operations numerical dropping is applied to maintain sparsity compared to previous methods this is a natural way to determine the sparsity pattern of the approximate inverse this paper describes newton global and column oriented algorithms and discusses options for initial guesses self preconditioning and dropping strategies some limited theoretical results on the properties and convergence of approximate inverses are derived numerical tests on problems from the harwell boeing collection and the fidap fluid dynamics analysis package show the strengths and limitations of approximate inverses finally some ideas and experiments with practical variations and applications are presented

adaptive sampled data integral control of stable infinite dimensional linear systems abstract in this paper adaptive discrete time low gain integral control strategies are presented for tracking constant reference signals for infinite dimensional discrete time power stable linear systems the discrete time results are applied in the development of adaptive sampled data low gain integral control of well posed infinite dimensional exponentially stable linear systems our results considerably extend improve and simplify previous work by two of the authors h logemann s townley discrete time low gain control of uncertain infinite dimensional systems ieee trans automat control 42 1997 22 37

on polynomial preconditioning and asymptotic convergence factors for indefinite hermitian matrices abstract we are concerned with the minimal residual method combined with polynomial preconditioning for solving large linear systems ax b with indefinite hermitian coefficient matrices a the standard approach for choosing the polynomial preconditioner leads to preconditioned systems which are positive definite here we investigate a different strategy which leaves the preconditioned coefficient matrix indefinite more precisely the polynomial preconditioner is designed to cluster the positive negative eigenvalues of a around 1 around some negative constant in particular it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of chebyshev approximation problems the problem of selecting the parameters so that the resulting indefinite polynomial preconditioner speeds up the convergence of the minimal residual method optimally is also addressed for this task we propose an approach based on the concept of asymptotic convergence factors finally some numerical examples of indefinite polynomial preconditioners are given

quadratic optimal control of stable well posed linear systems we consider the infinite horizon quadratic cost minimization problem for a stable time invariant well posed linear system in the sense of salamon and weiss and show that it can be reduced to a spectral factorization problem in the control space more precisely we show that the optimal solution of the quadratic cost minimization problem is of static state feedback type if and only if a certain spectral factorization problem has a solution if both the system and the spectral factor are regular then the feedback operator can be expressed in terms of the riccati operator and the riccati operator is a positive self adjoint solution of an algebraic riccati equation this riccati equation is similar to the usual algebraic riccati equation but one of its coefficients varies depending on the subspace in which the equation is posed similar results are true for unstable systems as we have proved elsewhere

a riesz basis methodology for proportional and integral output regulation of a one dimensional diffusive wave equation in this article we consider a dam river system modeled by a diffusive wave equation this model is commonly used in hydraulic engineering to describe dynamic behavior of the unsteady flow in a river for shallow water when the flow variations are not important in order to stabilize and regulate the system we propose a proportional and integral boundary controller contrary to many physical systems we end up with a nondissipative closed loop system with noncollocated actuators and sensors we show that the closed loop system is a riesz spectral system and generates an analytic semigroup then we shall be able to assign the spectrum of the closed loop system in the open left half plane to ensure its exponential stability as well as the output regulation independently of any known or unknown constant perturbation these results are illustrated by several numerical examples

a numerical experimental study of inverse preconditioning for the parallel iterative solution to 3d finite element flow equations integration of the subsurface flow equation by finite elements fe in space and finite differences fd in time requires the repeated solution to sparse symmetric positive definite systems of linear equations iterative techniques based on preconditioned conjugate gradients pcg are one of the most attractive tool to solve the problem on sequential computers a present challenge is to make pcg attractive in a parallel computing environment as well to this aim a key factor is the development of an efficient parallel preconditioner fsai factorized sparse approximate inverse and enlarged fsai relying on the approximate inverse of the coefficient matrix appears to be a most promising parallel preconditioner in the present paper pcg using fsai diagonal and parms parallel algebraic recursive multilevel solvers preconditioners is implemented on the ibm sp4 512 and clx 768 supercomputers with up to 32 processors to solve underground flow problems of a large size the results show that fsai may allow for a parallel relative efficiency e p larger than 50 on the largest problems with p 32 processors moreover fsai turns out to be significantly less expensive and more robust than parms finally it is shown that e p for p in the upper range may be much improved if pcg fsai is implemented on clx

polynomial preconditioners for conjugate gradient calculations dubois greenbaum and rodrigue proposed using a truncated neumann series as an approximation to the inverse of a matrix a for the purpose of preconditioning conjugate gradient iterative approximations to ax b if we assume that a has been symmetrically scaled to have unit diagonal and is thus of the form i g then the neumann series is a power series in g with unit coefficients the incomplete inverse was thought of as a replacement of the incomplete cholesky decomposition suggested by meijerink and van der vorst in the family of methods iccg n the motivation for the replacement was the desire to have a preconditioned conjugate gradient method which only involved vector operations and which utilized long vectors we here suggest parameterizing the incomplete inverse to form a preconditioning matrix whose inverse is a polynomial in g we then show how to select the parameters to minimize the condition number of the product of the polynomial and i g theoretically the resulting algorithm

polynomial preconditioning on vector computers abstract this paper is concerned with the computation of the minimal eigenpair of the generalized eigenproblem with the preconditioned conjugate gradient method the ssor polynomial preconditioner and the additive polynomial preconditioner have been analyzed the results of an extensive computer experimentation on cray y mp are reported

digital variable sampling integral control of infinite dimensional systems subject to input nonlinearity in this technical note we present a novel sampled data low gain i control algorithm for infinite dimensional systems in the presence of input nonlinearity the system is assumed to be exponentially stable with invertible steady state gain we use an integral controller with fixed integrator gain chosen on the basis of state gain information and a time varying sampling period determined by the growth bound of the system we compare this new algorithm with two other algorithms one with fixed gain and sampling period the other with time varying gain

infinite dimensional linear systems with unbounded control and observation a functional analytic approach abstract the object of these notes is to develop a unifying framework for the functional analytic representation of infinite dimensional linear systems with unbounded input and output operators on the basis of the general approach new results are derived on the wellposedness of feedback systems and on the linear quadratic control problem the implications of the theory for large classes of functional and partial differential equations are discussed in detail keywords representation of infinite dimensional systems semigroups boundary control feedback linear quadratic control

polynomial preconditioners based on factorized sparse approximate inverses let ax b be a linear system where a is a symmetric positive definite matrix an additive polynomial preconditioner for the conjugate gradient method based on multisplittings is proposed the multisplittings are obtained by computing some factorized sparse approximate inverses of the coefficient matrix namely splittings of the form a email protected email protected t 1 n email protected email protected t a 1 induced by the ainv and fsai factorized approximate inverse preconditioners applied to diagonal blocks of a are used the applicability of this preconditioner is studied moreover the results of the numerical experiments obtained on a cray t3e for a representative set of matrices are presented specifically structural analysis and transport diffusion problems are considered the effect of the reverse cuthill mckee rcm and multiple minimum degree mmd orderings is evaluated

the behavior of conjugate gradient algorithms on a multivector processor with a hierarchical memory abstract in this paper an analysis of some of the tradeoffs involved in the design and efficient implementation of conjugate gradient based algorithms for a multivector processor with a two level memory hierarchy is presented and supplemented by experimental results obtained on an alliant fx 8 the algorithms considered consist of the classical conjugate gradient method preconditioning techniques that are well suited for parallel computers such as polynomial preconditioners and several versions of the incomplete cholesky preconditioners as well as the reduced system approach for linear systems arising from the 5 point finite difference discretization of 2 d self adjoint elliptic p d e s the analysis shows that conjugate gradient methods do not perform as well as algorithms for dense matrix computations on the considered architecture due to lack of data locality by using the reduced system approach however a significant decrease in time could be obtained

on conjugate gradient type methods and polynomial preconditioners for a class of complex non hermitian matrices we consider conjugate gradient type methods for the solution of large linear systemsa x b with complex coefficient matrices of the typea t i i wheret is hermitian and a real scalar three different conjugate gradient type approaches with iterates defined by a minimal residual property a galerkin type condition and an euclidean error minimization respectively are investigated in particular we propose numerically stable implementations based on the ideas behind paige and saunder s symmlq and minres for real symmetric matrices and derive error bounds for all three methods it is shown how the special shift structure ofa can be preserved by using polynomial preconditioning and results on the optimal choice of the polynomial preconditioner are given also we report on some numerical experiments for matrices arising from finite difference approximations to the complex helmholtz equation

parallel preconditioning with sparse approximate inverses a parallel preconditioner is presented for the solution of general sparse linear systems of equations a sparse approximate inverse is computed explicitly and then applied as a preconditioner to an iterative method the computation of the preconditioner is inherently parallel and its application only requires a matrix vector product the sparsity pattern of the approximate inverse is not imposed a priori but captured automatically this keeps the amount of work and the number of nonzero entries in the preconditioner to a minimum rigorous bounds on the clustering of the eigenvalues and the singular values are derived for the preconditioned system and the proximity of the approximate to the true inverse is estimated an extensive set of test problems from scientific and industrial applications provides convincing evidence of the effectiveness of this approach

minimum phase infinite dimensional second order systems in general better performance can be achieved with a controlled minimum phase system than a controlled nonminimum phase system we show that a wide class of second order infinite dimensional systems with either velocity or position measurements are minimum phase the results are illustrated by two examples

low gain control of uncertain regular linear systems it is well known that closing the loop around an exponentially stable finite dimensional linear time invariant plant with square transfer function matrix bg s compensated by a controller of the form k s gamma 0 where k in bbb r and gamma 0 in bbb r mm will result in an exponentially stable closed loop system which achieves tracking of arbitrary constant reference signals provided that i all the eigenvalues of bg 0 gamma 0 have positive real parts and ii the gain parameter k is positive and sufficiently small in this paper we consider a rather general class of infinite dimensional linear systems called regular systems for which convenient representations are known to exist both in time and in frequency domain the purpose of the paper is twofold i we extend the above result to the class of exponentially stable regular systems and ii we show how the parameters k and gamma 0 can be tuned adaptively the resulting adaptive tracking controllers are not based on system identification or parameter estimation algorithms nor is the injection of probing signals required

on the incomplete cholesky decomposition of a class of perturbed matrices we consider how to cheaply compute an incomplete cholesky decomposition of symmetric perturbed matrices c epsilon i a with a small epsilon when knowing an incomplete decomposition of a numerical examples are provided that show the effectiveness of the proposed approach

properties of the semigroup and the approximation of crandall liggett associated with a class of differential equations with delays depending implicitly on the state abstract in this paper we are concerned with the semigroup properties and the crandall liggett approximation associated with a class of differential equations with delays depending implicitly on the state the existence of a strongly continuous nonlinear semigroup associated with the solutions of the equations is proved various properties of this semigroup have been established such as the continuous dependence the compactness and the infinitesimal generators an approximation of crandall liggett type has also been established

a semigroup approach to nonlinear nonautonomous neutral functional differential equations abstract a class of nonlinear nonautonomous neutral functional differential equations is studied by associating with it an evolution equation in the space of initial data the space w1 1 existence and regularity results are proved

parallel preconditioned conjugate gradient optimization of the rayleigh quotient for the solution of sparse eigenproblems a parallel algorithm based on the multidimensional minimization of the rayleigh quotient is proposed to evaluate the leftmost eigenpairs of the generalized symmetric positive definite eigenproblem the minimization is performed via a conjugate gradient like procedure accelerated by a factorized approximate inverse preconditioner fsai and by a number of block preconditioners the resulting code obtains a high level of parallel efficiency and proves to be comparable with the parpack package on a set of large matrices arising from various discretizations of pdes of elliptic parabolic type