a connection between state space and doubly coprime fractional representations explicit formulas for a doubly coprime fractional representation of the transfer function of a lumped lti system are given in terms of a stabilizable and detectable state space realization of the transfer function these formulas allow existing computational algorithms to be utilized for the purpose of computing doubly coprime factorizations several additional implications of this result are briefly discussed as are some immediate extensions and future research directions

system identification method by using inverse solution of equations of motion in time domain and noisy condition abstract in direct system identification dsi method inverse solution of the equations of motion is applied to obtain physical parameters of a linear system structural mass damping and stiffness matrices with the small error in measurement caused by sensor drift or signal noise these physical parameters are identified with a significant drift in this paper a new simple post processing method is proposed for error reduction in dsi in the time domain in a manner that structural properties are identified without applying the optimization process in noisy condition baseline correction is applied through a nonic curve fitting approach the modified signals are partitioned into a number of sub signals and their mean is applied for system identification the number of sub signals is optimized so that the root mean square rms of off diagonal components of the mass matrix becomes near zero seeking more precision the residual force in every time step at all degrees of freedom dofs is minimized the validity of the proposed method is tested on a multistory structure subjected to a random force at the foundation level in terms of incomplete measurement and 5 noise identified parameters including mass stiffness and damping matrices have satisfying mean errors of 0 094 0 545 and 4 42 with the coefficient of variations of 0 35 1 38 and 6 98 respectively the sensitivity of the proposed method to the noise level is also investigated it is observed that the baseline slop of velocity and displacement signals are sharply increased when the noise level goes beyond 3

the perturbation theory for the drazin inverse and its applications abstract let a and e be n n matrices and b a e denote the drazin inverse of a by ad we give an upper bound for the relative error b d a d a d under certain circumstances an error bound for the solution for the singular equations ax b b r a is also considered

index splitting for the drazin inverse and the singular linear system abstract an index splitting of a singular matrix a for the drazin inverse and its relative iterations for the minimal p norm solution of the singular linear system ax b b r a k k ind a are presented some convergence criteria are also given and a method is developed for constructing the index splitting of matrix a

a family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non square matrix based on a quadratical convergence method a family of iterative methods to compute the approximate inverse of square matrix are presented the theoretical proofs and numerical experiments show that these iterative methods are very effective and more importantly these methods can be used to compute the inner inverse and their convergence proofs are given by fundamental matrix tools

successive matrix squaring algorithm for computing the drazin inverse1this project is supported by the national nature science foundation of china doctoral point foundation of china and youth science foundation of universities in shanghai of china 1 this paper derives a successive matrix squaring sms algorithm to approximate the drazin inverse which can be expressed in the form of successive squaring of a composite matrix t given an n by n matrix a the study shows that the drazin inverse of a can be computed in parallel time ranging from o logn to o log 2n provided that there are enough processors to support matrix multiplication in time o logn the sms algorithm is generalized to higher order schemes where the composite matrix is repeatedly raised to an integer power l 2 this form of expression leads to a simplified notation compared to that of earlier methods we argue that there is no obvious advantage in choosing l other than 2 our derived error bound for the approximation of a d is new

an oblique projection iterative method to compute drazin inverse and group inverse in this paper an oblique projection iterative method is presented to compute matrix equation axa a of a square matrix a with ind a 1 by this iterative method when taken the initial matrix x 0 a the group inverse a g can be obtained in absence of the roundoff errors if we use this iterative method to the matrix equation a kxa k a k a group inverse a k g of matrix a k is got then we use the formulae a d a k 1 a k g the drazin inverse a d can be obtained

symbolic computation of drazin inverses by specializations in this paper we show how to reduce the computation of drazin inverses over certain computable fields to the computation of drazin inverses of matrices with rational functions as entries as a consequence we derive a symbolic algorithm to compute the drazin inverse of matrices whose entries are elements of a finite transcendental field extension of a computable field the algorithm is applied to matrices over the field of meromorphic functions in several complex variables on a connected domain and to matrices over the field of laurent formal power series

squaring down lti systems a geometric approach in this paper the problem of reducing a given lti system into a left or right invertible one is addressed and solved with the standard tools of the geometric control theory first it will be shown how an lti system can be turned into a left invertible system thus preserving key system properties like stabilizability phase minimality right invertibility relative degree and infinite zero structure moreover the additional invariant zeros introduced in the left invertible system thus obtained can be arbitrarily assigned in the complex plane by duality the scheme of a right inverter will be derived straightforwardly moreover the squaring down problem will be addressed in fact when the left and right reduction procedures are applied together a system with an unequal number of inputs and outputs is turned into a square and invertible system furthermore as an example it will be shown how these techniques may be employed to weaken the standard assumption of left invertibility of the plant in many optimization problems

special coordinate basis for multivariable linear systems finite and infinite zero structure squaring down and decoupling abstract a special coordinate basis for multivariable linear systems is introduced here several fundamental properties of linear systems regarding controllability stabiliza bility observability detectability invariant zeros decoupling zeros infinite zero structure effect of feedback on zero structure squaring down diagonal and triangular decoupling etc can be directly displayed in terms of the special coordinate basis moreover connections between the special coordinate basis and the important invariant subspaces of the geometric theory of linear systems are established

complexity of parallel matrix computations abstract we estimate parallel complexity of several matrix computations under both boolean and arithmetic machine models using deterministic and probabilistic approaches those computations include the evaluation of the inverse the determinant and the characteristic polynomial of a matrix recently processor efficiency of the previous parallel algorithms for numerical matrix inversion has been substantially improved in pan and reif 1987 reaching optimum estimates up to within a logarithmic factor that work however applies neither to the evaluation of the determinant and the characteristic polynomial nor to exact matrix inversion nor to the numerical inversion of ill conditioned matrices we present four new approaches to the solution of those latter problems having several applications to combinatorial computations in order to extend the suboptimum time and processor bounds of pan and reif 1987 to the case of computing the inverse determinant and characteristic polynomial of an arbitrary integer input matrix in addition processor efficient algorithms using polylogarithmic parallel time are devised for some other matrix computations such as triangular and qr factorizations of a matrix and its reduction to hessenberg form

squaring down descriptor systems constructive solutions and numerical algorithms we consider the problem of squaring down a general descriptor linear time invariant system squaring down consists in finding a pre and a post compensator such that the system is turned into a square invertible one we consider three classes of solutions static dynamic and norm preserving all characterization are made by using generalized state space realizations while the associated computations are performed by employing orthogonal transformations and standard reliable procedures for eigenvalue assignment usual benefits of classical squaring down schemes like the stability of the designed compensators or preservation of minimum phase stabilizability detectability and the infinite zero structure of the original system are recovered as well

structural stability of lattice boltzmann schemes the goal of this work is to determine classes of traveling solitary wave solutions for lattice boltzmann schemes by means of an hyperbolic ansatz it is shown that spurious solitary waves can occur in finite difference solutions of nonlinear wave equation the occurence of such a spurious solitary wave which exhibits a very long life time results in a non vanishing numerical error for arbitrary time in unbounded numerical domain such a behavior is referred here to have a structural instability of the scheme since the space of solutions spanned by the numerical scheme encompasses types of solutions solitary waves in the present case that are not solutions of the original continuous equations this paper extends our previous work about classical schemes to lattice boltzmann schemes 1 2 3 4

the hyperpower iteration revisited the hyperpower method is generalized by inseting an idempotent matrix p it is shown that most of the iterations that can be used for computing generalized inverses can be recast in this form by suitable choice of the idempotent the limit or the initial values the convergence behavior of bqk is analyzed and the results are applied to give a detailed investigation of this iteration

on the solution of singular linear systems of algebraic equations by semiiterative methods for a square matrixt n n where i t is possibly singular we investigate the solution of the linear fixed point problemx tx c by applying semiiterative methods sim s to the basic iterationx0 n xk tck 1 c k 1 such problems arise if one splits the coefficient matrix of a linear systemax b of algebraic equations according toa m n m nonsingular which leads tox m 1nx m 1b tx c even ifx tx c is consistent there are cases where the basic iteration fails to converge namely ift possesses eigenvalues 1 with 1 or if 1 is an eigenvalue oft with nonlinear elementary divisors in these cases and also ifx tx c is incompatible we derive necessary and sufficient conditions implying that a sim tends to a vector hat x which can be described in terms of the drazin inverse of i t we further give conditions under which hat x is a solution or a least squares solution of i t x c

synthesis of positive real multivariable feedback systems this is a tutorial paper describing the application of infinity norm optimal control theory to the synthesis of sector bounded and positive real multivariable feedback systems the paper gives a concise treatment of the practical aspects of the theory describing how it has been implemented via state space oriented computer algorithms included is a concise summary of the state space approach to infinity norm control developed by doyle and by safonov and verma based on the hankel model reduction theory and incorporating the multivariable hankel results of glover

squaring down by static and dynamic compensators given a system which is not necessarily invertible and which has an unequal number of inputs a method of squaring down that is a method of designing pre compensators and postcompensators such that the resulting system has an equal number of inputs and outputs and is invertible is presented the compensators are in general dynamic and have the property that the additional finite zeros induced by them are assignable to the open left half complex plan furthermore the compensators are asymptotically stable and hence do not deteriorate the robustness and performance of an eventual feedback design also the compensator design preserves the stabilizability detectability and minimum phase properties and the infinite zero structure of the original system thus a method of designing nonsquare systems by converting them to square invertible systems is introduced two applications of such a design philosophy 1 diagonal decoupling with state feedback and 2 almost disturbance decoupling with output feedback are pointed out

squaring down with zeros cancellation in generalized systems squaring down with simultaneous zeros cancellation by series compensation of a general possibly polynomial or improper linear system is investigated all static and dynamical compensators that spotlight minimal mcmillan degree are parameterized this general result is particularized to get compensators that preserve the l 2 or l inf norm of the original system either in continuous or discrete time all results are completely general numerically sound and based on general realizations allowing for poles at infinity

successive matrix squaring algorithm for computing outer inverses abstract in this paper we derive a successive matrix squaring sms algorithm to approximate an outer generalized inverse with prescribed range and null space of a given matrix a c r m n we generalize the results from the papers l chen e v krishnamurthy i macleod generalized matrix inversion and rank computation by successive matrix powering parallel computing 20 1994 297 311 y wei successive matrix squaring algorithm for computing drazin inverse appl math comput 108 2000 67 75 y wei h wu j wei successive matrix squaring algorithm for parallel computing the weighted generalized inverse a mn appl math comput 116 2000 289 296 and obtain an algorithm for computing various classes of outer generalized inverses of a instead of particular matrices used in these articles we use an appropriate matrix r c s n m s r numerical examples are presented

successive overrelaxation methods for solving the rank deficient linear squares problem abstract we develop successive overrelaxation sor methods for finding the least squares solution of minimal norm to the system ax b where a is an m n matrix of rank r the methods are obtained by first augmenting the system to a block 4 4 consistent system of linear equations the augmented coefficient matrix is then split by a subproper sor splitting an interval for the relaxation parameter in which the subproper sor iteration matrix is semiconvergent is determined along with the optimal relaxation parameter which minimizes the modulus of the controlling eigenvalue of the sor matrix since the scheme computes at first only a solution to the augmented system it is subsequently shown how to transform such a solution to the unique solution of minimal 2 norm analysis of the practical implementation of the algorithms developed here will be given elsewhere

structured perturbations of drazin inverse in this paper the normwise perturbation theory of the drazin inverse is investigated we study the following structure matrices toeplitz hankel matrices when we take the structure of the matrix we get that the structured condition number is small compared with unstructured condition number for specific right hand side we give the estimate and formula of the condition number for structured system

numerical investigation of the pseudopotential lattice boltzmann modeling of liquid vapor for multi phase flows abstract the incorporation of different equations of state into single component multiphase lattice boltzmann model is considered in this paper the original pseudopotential model is first detailed and several cubic equations of state the redlich kwong redlich kwong soave and peng robinson are then incorporated into the lattice boltzmann model a comparison of the numerical simulation achievements on the basis of density ratios and spurious currents is used for presentation of the details of phase separation in these non ideal single component systems the paper demonstrates that the scheme for the inter particle interaction force term as well as the force term incorporation method matters to achieve more accurate and stable results the velocity shifting method is demonstrated as the force term incorporation method among many with accuracy and stability results kupershtokh scheme also makes it possible to achieve large density ratio up to 1 0 4 and to reproduce the coexistence curve with high accuracy significant reduction of the spurious currents at vapor liquid interface is another observation high density ratio and spurious current reduction resulted from the redlich kwong soave and peng robinson eoss in higher accordance with the maxwell construction results

a cramer rule for finding the solution of a class of singular equations a cramer rule for finding the unique solution x r ak of singular equations ax b ind a k b r ak is given and reduces to the common cramer rule if a is a nonsingular

state space formulae for all stabilizing controllers that satisfy and h norm bound and relations to risk sensitivity abstract given a linear system all stabilizing controllers such that a specified closed loop transfer function has h norm less than a given scalar are parametrized this characterization involves the solution to two algebraic riccati equations each with the same order as the system and further gives gives feasible controllers also with this order the relationship to the risk sensitive lqg stochastic control problem is established giving an equivalence between robust and stochastic control

squaring down and the problems of almost zeros for continuous time systems abstract in this paper we construct precompensators which square down a system such that the resulting square system has the same unstable zeros and system gains we derive the minimal gain of the precompensator to achieve such a square system if the gain of this precompensator is too large then we derive an explicit trade off between the gain of the precompensator and the number of unstable zeros we allow the precompensator to introduce in the system

a schur method for balanced truncation model reduction it is shown that a not necessarily balanced state space realization of the moore reduced model can be computed directly without balancing via projections defined in terms of arbitrary bases for the left and right eigenspaces associated with the large eigenvalues of the product pq of the reachability and controllability grammians two specific methods for computing these bases are proposed one based on the ordered schur decomposition of pq and the other based on the cholesky factors of p and q the algorithms perform reliably even for nonminimal models

on the perturbation of the group inverse and oblique projection for given matrices a and e which are n matrices and matrices and e we discuss upper bounds for b bb b a a and bb aa aa also a lower bound for b is derived

the drazin inverse in multibody system dynamics the numerical analysis of multibody system dynamics is based on the equations of motion as differential algebraic systems a thorough analysis of the linearized equations and their solution theory leads to an equivalent system of ordinary differential equations which gives deeper insight into the derivation of integration schemes and into the stabilization approaches the main tool is the drazin inverse a generalized matrix inverse which preserves the eigenvalues the results are illustrated by a realistic truck model finally the approach is extended to the nonlinear index 2 formulation

rational matrix gcds and the design of squaring down compensators a state space theory a state space construction for rational matrix greatest common divisors gcds of rational transfer matrices is given it is shown how the gcd results can be used to solve the problem of designing stable minimum phase squaring down compensators for multi variable plants one application is a direct state space construction for such compensators and a state space solution to fat plant h infinity control problems the results make use of the concepts of strongly observable systems and maximally observable systems and build upon the concepts introduced in the state space gcd extraction results for polynomial matrices of l m silverman and p van dooren 1979

a complete and simple parametrization of controllers for a nonstandard h control problem abstract a complete and simple parametrization of all h controllers is derived for a class of nonstandard h control problems with d 12 and d 21 being of full row and column ranks respectively by making use of the youla parametrization and standard h control theory

regular article calculation of two phase navier stokes flows using phase field modeling phase field models provide a way to model fluid interfaces as having finite thickness this can allow the computation of interface movement and deformation on fixed grids this paper applies phase field modeling to the computation of two phase incompressible navier stokes flows the navier stokes equations are modified by the addition of the continuum forcing email protected f where c is the composition variable and f is c s chemical potential the equation for interface advection is replaced by a continuum advective diffusion equation with diffusion driven by c s chemical potential gradients the paper discusses how solutions to these equations approach those of the original sharp interface navier stokes equations as the interface thickness e and the diffusivity both go to zero the basic flow physics of phase field interfaces is discussed straining flows can thin or thicken an interface and this must be resisted by a high enough diffusion on the other hand too large a diffusion will overly damp the flow these two constraints result in an upper bound for the diffusivity of o e and a lower bound of o e 2 within these two bounds the phase field navier stokes equations appear to generate an o e error relative to the exact sharp interface equations an o h 2 e 2 numerical method is introduced that is energy conserving in the sense that creation of interface energy by convection is always balanced by an equal decrease in kinetic energy caused by surface tension forcing an o h 4 e 4 compact scheme is introduced that takes advantage of the asymptotic comparatively smooth behavior of the chemical potential for o e accurate phase field models the optimum path to convergence for this scheme appears to be email protected 4 5 the asymptotic rate of convergence corresponding to this is o h 4 5 but results at practical resolutions show that the practical convergence of the method is generally considerably faster than linear extensive analysis and computations show that this scheme is very effective and accurate it allows the accurate calculation of two phase flows with interfaces only two cells wide computational results are given for linear capillary waves and for rayleigh taylor instabilities the first set of computations is compared to exact solutions of the diffuse interface equations and of the original sharp interface equations the rayleigh taylor computations test the ability of the method to compute highly deforming flows these flows include near singular phenomena such as interface coalescences and breakups contact line movement and the formation and breakup of thin wall films grid refinement studies are made and rapid convergence is found for macroscopic flow features such as instability growth rate and propagation speed wavelength and the general physical characteristics of the instability and mass transfer rates

generalized inverses and a block rank equation for a square matrix a of index 1 the block rank equationrankabcx rank a is studied geometrical conditions are given to characterize the solution of this equation further all matrices b and c are described for the solution x a where a is the group inverse of a in addition we extend these results to reflexive generalized inverses this contributes to a result recently obtained by wei siam j matrix anal appl 17 1996 744 and it is a generalization of a result by grosz lin alg appl 289 1999 127

fast and efficient parallel solution of dense linear systems the most efficient previously known parallel algorithms for the inversion of a nonsingular n n matrix a or solving a linear system ax b over the rational numbers require o log2n time and m n n processors provided that m n processors suffice in order to multiply two n n rational matrices in time o logn furthermore the known polylog arithmetic time algorithms for those problems are numerically unstable in this paper we apply newton s iteration and initially choose an approximate inverse matrix by following ben israel this quadratically convergent and numerically stable iterative method takes o log2n parallel time using m n processors to compute the inverse within the relative precision 2 nc for a positive constant c of an n n rational matrix a with the condition number at most nd for a constant d this is the optimum processor bound and by a factor of n improvement of the previously known processor bounds for polylogarithmic time matrix inversion the algorithm does not require to precompute the condition number of the input matrix but it just converges slower for ill conditioned input matrices

preconditionings and splittings for rectangular systems recently eiermann marek and niethammer have shown how to applysemiiterative methods to a fixed point systemx tx c which isinconsistent or in whichthe powers of the fixed point operator t have no limit to obtain iterative methods which converge to some approximate solution to the fixed point system in view of their results we consider here stipulations on apreconditioning qax qb of the systemax b and separately on asplitting a m n which lead to fixed point systems such that with the aid of a semiiterative method the iterative scheme converges to a weighted moore penrose solution to the systemax b we show in several ways that to obtain a meaningful limit point from a semiiterative method requires less restrictions on the splittings or the reconditionings than those which have been required in the classical picard iterative method see e g the works of berman and plemmons berman and neumann and tanabe we pay special attention to the case when the weighted moore penrose solution which is sought is the minimal norm least squares solution toax b

finite precision behavior of stationary iteration for solving singular systems a stationary iterative method for solving a singular system ax b converges for any starting vector if limi gi exists where g is the iteration matrix and the solution to which it converges depends on the starting vector we examine the behavior of stationary iteration in finite precision arithmetic a pertubation bound for singular systems is derived and used to define forward stability of a numerical method a rounding error analysis enables us to deduce conditions under which a stationary iterative method is forward stable or backward stable the component of the forward error in the null space of a can grow linearly with the number of iterations but it is innocuous as long as the iteration converges reasonably quickly as special cases we show that when a is symmetric positive semidefinite the richardson iteration with optimal parameter is forward stable and if a also has unit diagonal and property a then the gauss seidel method is both forward and backward stable two numerical examples are given to illustrate the analysis

luenberger observer based h sub spl infin compensator design for nonstandard problems this paper presents luenberger observer based h sub spl infin compensator design methods for different nonstandard cases these design methods are developed based on the bounded real lemma and the resultant design algorithms are two riccati inequalities which are not mutually coupled

a novel nonlinear regression model of svr as a substitute for ann to predict conductivity of mwcnt cuo water hybrid nanofluid based on empirical data abstract an ideal regression method should have several characteristics including precision accuracy and generalization in many studies in the field of nanofluid the precision of models is more highlighted nevertheless a lack of generalization may lead to over fitted models in this paper two nonlinear regression methods namely the ann and svr are employed to predict the thermal conductivity of mwcnt cuo water hybrid nanofluid with temperature and volume fraction it is seen that precision of svr ann approaches are able to be compared however svr generalization is more convenient compared to ann because svr method utilizes less parameters hence svr can show better persistence to overfitting in little size datasets compared to ann therefore svr is more authentic approach for the regression with little size datasets