statistical analysis of the least squares autoregressive estimator in the presence of noise this paper analyzes the asymptotic statistical properties of the least squares autoregressive ar estimator in the presence of noise the asymptotic covariance of this estimator is derived for an ar signal with additive white or colored noise the result is shown to hold for a general gaussian or linear stationary measurement the analysis is applied in detail to first order systems a procedure for using the result to solve problems in speech recognition biomedical diagnosis and fault detection is presented results of simulations confirm the theoretical analysis

dgmres a gmres type algorithm for drazin inverse solution of singular non symmetric linear systems abstract in a recent work by the author linear algebra appl 298 1999 99 krylov subspace methods were derived for drazin inverse solution of consistent or inconsistent linear systems of the form ax b where a c n n is a singular and in general non hermitian matrix that has arbitrary index one of these methods modeled after the generalized conjugate residual method gcr and denoted dgcr is considered in the present work again it is shown that all of the approximations produced by dgcr exist and a gmres like algorithm denoted dgmres for its implementation is derived like gmres dgmres too is economical computationally and storagewise

displacement rank of the drazin inverse in this paper we study the displacement rank of the drazin inverse both sylvester displacement and the generalized displacement are discussed we present upper bounds for the ranks of the displacements of the drazin inverse the general results are applied to the group inverse of a structured matrix such as close to toeplitz generalized cauchy toeplitz plus hankel and bezoutians

displacement structure for hankel vandermonde and related derived matrices abstract we introduce some generalized concepts of displacement structure for structured matrices obtained as products and inverses of toeplitz hankel and vandermonde matrices the toeplitz case has already been studied at some length and the corresponding matrices have been called near toeplitz or toeplitz like or toeplitz derived we focus on hankel and vandermonde like matrices and in particular show how the appropriately defined displacement structure yields fast triangular and orthogonal factorization algorithms for such matrices the main contribution of this paper is presenting a unified framework rather than obtaining the fastest algorithm for each special matrix

extended chandrasekhar recursions we extend the discrete time chandrasekhar recursions for least squares estimation in constant parameter state space models to a class of structured time variant state space models special cases of which often arise in adaptive filtering it can be shown that the much studied exponentially weighted recursive least squares filtering problem can be reformulated as an estimation problem for a state space model having this special time variant structure other applications arise in the multichannel and multidimensional adaptive filtering context

iterative inversion of structured matrices iterative processes for the inversion of structured matrices can be further improved by using a technique for compression and refinement via the least squares computation we review such processes and elaborate upon incorporation of this technique into the known frameworks

displacement structure of w weighted drazin inverse ad w and its perturbation it is well known that matrices with a uv displacement structure possess generalized inverse with a vu displacement structure estimations for the displacement rank of a d wu va d w are presented where a d w is the w weighted drazin inverse of a we extend the results for the drazin inverse and group inverse respectively in the end the perturbation of w weighted drazin inverse a d w is studied

generalized inverse a 2 t s and a rank equation in this paper the rank equationrankabcx rank a is considered in the sense that b and c are characterized when a 2 t s is solution to this equation as the special cases similar results for a a m n a d and a g are also derived this contributes to certain recent results in the literature including that obtained by grosz linear algebra appl 289 1999 127 and thome and wei appl math comput 141 2003 471

on the solution of the minimal rational interpolation problem it is shown that the reachability and the observability indices of appropriately defined pairs of matrices provide the key for solving the minimal rational bitangen tial interpolation problem

a look ahead levinson algorithm for general toeplitz systems the authors present an extension of levinson s algorithm that is guaranteed to be weakly stable for a large class of general toeplitz matrices namely those that do not have many consecutive ill conditioned leading principal submatrices the new algorithm adapts itself to the given toeplitz matrix by skipping over all the ill conditioned leading principal submatrices encountered during the solution process this is done by a look ahead strategy that monitors the condition of the leading principal submatrices and if necessary switches to a block step of suitable size the overhead of the look ahead algorithm is typically small compared to the classical levinson algorithm and in addition a reliable condition number estimate is produced

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

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

the 2 inverse with applications in statistics an inverse g of a given matrix a which satisfies the property gag g is known as a 2 inverse this paper presents a three phase inversion procedure for which the 2 inverse is a special case we present the geometry of 2 inverses and show that starting from 2 inverses various types of generalized inverses can be derived two examples of the occurrence of 2 inverses in statistics are given one concerning the constrained least squares estimator the other concerning a necessary and sufficient condition for a quadratic form of singular multivariate normal variates to follow a chi square distribution

hankel and loewner matrices abstract mutual relations between the hankel toeplitz bezout and loewner matrices as well as further connections to rational interpolation and projective geometry are investigated

position feedback global tracking control of el systems a state transformation approach the contribution of this paper is a dynamic position feedback global tracking controller for fully actuated euler lagrange el systems the properties we show for the closed loop system are uniform stability and exponential convergence global in the initial tracking errors and semiglobal in the initial estimation errors the novelty of our approach is that our observer and control design are based on a new model for el systems which is linear in the immeasurable velocities this model is shown to fit robot manipulators we also provide some simulation results

the representation and approximation for drazin inverse we present a unified representation theorem for drazin inverse specific expression and computational procedures for drazin inverse can be uniformly derived numerical examples are tested and the application to the singular linear equations is also considered

on group inverse of singular toeplitz matrices in this paper we show that the group inverse of a real singular toeplitz matrix can be represented as the sum of products of lower and upper triangular toeplitz matrices such a matrix representation generalizes gohberg semencul formula in the literature

fast recursive identification of state space models via exploitation of displacement structure abstract the seemingly computational burden of state space model identification has limited its real time application though it offers some important advantages over methods based on input output transfer functions it has been shown recently that ideas from the theory of displacement structure can be used in state space identification to reduce the computational burden of batch processing from o mn 2 to o mn flops when the data matrix is of size m n where n m however in many on line identification scenarios with slowly time varying systems it is desirable to update the model as time goes on with the minimal computational burden in this paper we extend our results of the batch processing algorithm to allow updating of the identified state space model with o m 2 flops again the theories of displacement structure and of the fast subspace decomposition fsd technique play crucial roles in the realization of the fast updating algorithm some computer simulation results are also presented

displacement structure of pseudoinverses abstract a matrix or a linear operator a is said to possess an uv displacement structure if rank au va is small compared with the rank of a estimates for the rank of a v ua and more general displacements of a are presented where a is the pseudoinverse of a the general results are applied to close to toeplitz close to vandermonde and generalized cauchy matrices bezoutians toeplitz and hankel operators singular integral operators and integral operators with displacement kernel this leads to formulas for a which can be used for the fast computation of pseudosolutions for vandermonde matrices the exact displacement rank of a is evaluated it turns out that this rank is not always small

the representation and approximation of the drazin inverse of a linear operator in hilbert space we present a unified representation theorem for the drazin inverse of linear operators in hilbert space and a general error bound five specific expressions computational procedures and their error bounds for the drazin inverse are uniformly derived from the unified representation theorem

an interpolation theory approach to h controller degree bounds abstract we derive upper bounds for the mcmillan degree of all h optimal controllers associated with design problems which may be embedded in a certain generalized regular configuration our analysis is confined to problems of the first kind which are characterized by the assumption that both p12 s and p21 s are square but not necessarily of the same size this paper which uses interpolation theory complements a previous paper which addresses the same problem through an approach based on approximation theory we demonstrate that the interpolation theory approach is more direct and circumvents a number of the technical difficulties in the previous method the final outcome is a much shorter proof as a by product we achieve a new result on the degree of an optimal solution of the matrix nevanlinna pick problem

hyperbolic householder transformations a class of transformation matrices analogous to the householder matrices is developed with a nonorthogonal property designed to permit the efficient deletion of data from least squares problems these matrices which we term hyperbolic householder are shown to effect deletion or simultaneous addition and deletion of data with much less sensitivity to rounding errors than for techniques based on normal equations when the addition deletion sets are large this numerical robustness is obtained at the expense of only a modest increase in computations and when only a relatively small fraction of the data set is modified there is a decrease in required computations two applications to signal processing problems are considered first these transformations are used to obtain a square root algorithm for windowed recursive least squares filtering second the transformations are employed to implement the rejection of spurious data from the weight vector estimator in an adaptive array

fast matrix factorizations via discrete transmission lines abstract fast algorithms associated with the names of schur and levinson are known for the triangular factorization of symmetric positive definite toeplitz matrices and their inverses in this paper we show that these algorithms can be derived from simple arguments involving causality symmetry and energy conservation in discrete lossless transmission lines the results not only provide a nice interpretation of the classical schur and levinson algorithms and a certain toeplitz inversion formula of gohberg and semencul but they also show immediately that the same fast algorithms apply not only to toeplitz matrices but to all matrices with so called displacement inertia 1 1 the results have been helpful in suggesting new digital filter structures and in the study of nonstationary second order processes

the one dimensional inverse problem of reflection seismology an impulsive normal traction is applied uniformly over the surface of a perfectly stratified plane layered earth the ensuing particle velocity at the surface is assumed to be measured the problem of calculating the subsurface characteristic impedance from knowledge of the input pulse and the measured data is the one dimensional inverse problem of reflection seismology the problem is set up mathematically as an inverse problem for a first order 2 times 2 hyperbolic system the role of propagation of singularities is explained and the relation between the solution of the inverse problem and the cholesky factorization of certain matrices constructed from the data is elaborated for both the continuum problem and the related discrete problem it is found that recursive numerical techniques such as the levinson algorithm and certain other fast methods for cholesky factorization are intimately related to explicit finite difference schemes for solving hyperbolic systems the order of approximation between the

stabilized hyperbolic householder transformations a modification of the hyperbolic householder scheme is introduced which is demonstrably stable theoretically according to an established stability criterion and which exhibits superior numerical behavior in simulations the modified transform scheme effects downdating by applying conventional orthonormal rather than hyperbolic householder transformations to the data the latter have preferable numerical properties however the construction of these orthonormal operators itself requires hyperbolic computations thus the proposed method is in some sense half hyperbolic and half orthonormal there is no computational penalty incurred with these stabilized hyperbolic householder transforms they enjoy an operation count identical to their conventional counterparts

condition number for the drazin inverse and the drazin inverse solution of singular linear system with their condition numbers in this paper we investigate the condition number of drazin inverse and drazin inverse solution of singular linear system ax b where a is a nxn rank deficient matrix and b a real vector of size n x a real vector let a and b be two positive real numbers when we consider the weighted frobenius norm aa bb p q f on the data we get the formula of condition number of the drazin inverse solution of singular linear system for the normwise condition number the sensitivity of the relative condition number itself is studied the componentwise perturbation is also investigated

remarks on the origin of the displacement rank concept an account is given of how a relationship was found between some equations of chandrasekhar for solving the wiener hopf integral equations and the nonlinear riccati differential equations encountered in linear least squares estimation problems for systems described in state space form a paper by casti kalaba and murthy 1972 provided the inspiration for seeking such a relationship and then extending it and applying it in many other fields using the concept of displacement structure

on drazin inverse of singular toeplitz matrix in this paper we show that the drazin inverse of singular toeplitz matrix can be represented as a sum of products of lower and upper triangular toeplitz matrices and give the explicit expression which generalizes the well known result by gohberg and semencul regarding the inverse of toeplitz matrix

generalized chandrasekhar recursions from the generalized schur algorithm presents a new approach to the chandrasekhar recursions and some generalizations thereof the derivation uses the generalized schur recursions which are o n sup 2 recursions for the triangular factorization of n spl times n matrices having a certain toeplitz like displacement structure it is shown that when the extra structure provided by an underlying state space model is properly incorporated into the generalized schur algorithm it reduces to the chandrasekhar recursions which are o nn sup 2 recursions for estimating the n dimensional state of a time invariant or constant parameter system from n measured outputs it is further noted that the generalized schur algorithm factors more general structured matrices and this fact is readily used to extend the chandrasekhar recursions to a class of time variant state space models special cases of which often arise in adaptive filtering

asymptotic second order properties of sample partial correlations the asymptotic behavior of the sample partial correlations parcors is studied in the case of a general stationary process an explicit formula for parcor s second order moments is provided the analysis presented extends to more general processes as shown using previously reported results on the statistics of sample partial correlations of autoregressive ar and mixed autoregressive moving average arma processes this extension should be useful as the processes encountered in applications are not exactly ar or arma

modified sms method for computing outer inverses of toeplitz matrices we introduce a new algorithm based on the successive matrix squaring sms method this algorithm uses the strategy of e displacement rank in order to find various outer inverses with prescribed ranges and null spaces of a square toeplitz matrix using the idea of displacement theory which decreases the memory space requirements as well as the computational cost our method tends to be very effective for toeplitz matrices

structured perturbations of group inverse and singular linear system with index one in this paper we study the normwise perturbation theory of singular linear structured system with index one the structures under investigation are toeplitz circulant hankel matrices we show that the structured condition number is smaller than unstructured condition number for specific right hand side we present the condition number for structured system

approximate iterations for structured matrices important matrix valued functions f a are e g the inverse a 1 the square root sqrt a and the sign function their evaluation for large matrices arising from pdes is not an easy task and needs techniques exploiting appropriate structures of the matrices a and f a often f a possesses this structure only approximately however intermediate matrices arising during the evaluation may lose the structure of the initial matrix this would make the computations inefficient and even infeasible however the main result of this paper is that an iterative fixed point like process for the evaluation of f a can be transformed under certain general assumptions into another process which preserves the convergence rate and benefits from the underlying structure it is shown how this result applies to matrices in a tensor format with a bounded tensor rank and to the structure of the hierarchical matrix technique we demonstrate our results by verifying all requirements in the case of the iterative computation of a 1 and sqrt a

on global uniform asymptotic stability of nonlinear time varying systems in cascade abstract in this short paper we deal with the stability analysis problem of nonautonomous nonlinear systems in cascade in particular we give sufficient conditions to guarantee that i a globally uniformly stable gus nonlinear time varying nltv system remains gus when it is perturbed by the output of a globally uniformly asymptotically stable guas nltv system under the assumption that the perturbing signal is absolutely integrable ii if in addition the perturbed system is guas it remains guas under the cascaded interconnection iii two guas systems yield a guas cascaded system under some growth restrictions over the lyapunov function our proofs rely on the second method of lyapunov roughly speaking on a e stability analysis

displacement structure of the generalized inverse a t s 2 it is well known that matrices with a uv displacement structure possess generalized inverse with a vu displacement structure estimation for the displacement rank of a t s 2 u va t s 2 are presented where a t s 2 is the 2 inverse of a we extend the results due to heinig and hellinger in 1994

inverse scattering for discrete transmission line models this paper presents several methods for the identification of the impedance and reflection coefficient profile of a nonuniform discrete transmission line from its response to a given forcing function this problem is the prototype for a wealth of one dimensional inverse scattering problems arising in various fields a unified straightforward approach is presented providing all known inversion procedures and some novel ones the derivations readily follow from causality of signal propagation on the transmission line it is shown that a direct exploitation of the signal propagation model leads to recursive computationally efficient and reliable inversion algorithms in particular the relationships between layer peeling schur type difference equation and layer adjoining levinson type integral equation algorithms are clearly displayed

a schur algorithm and linearly connected processor array for toeplitz plus hankel matrices a levinson durbin type algorithm for solving toeplitz plus hankel t h linear systems of equations is used to induce a schur type algorithm for such systems a schur type algorithm is defined as one which efficiently computes the ldu decomposition of the matrix on the other hand levinson durbin type algorithms are defined as those algorithms which efficiently compute the udl decomposition of the inverse of a matrix it is shown that the schur algorithm so obtained is amenable to efficient implementation on a linearly connected array of processors in a manner which generalizes the results of s y kung and y h ku 1983 for symmetric toeplitz matrices specifically if t h is of order n then the schur algorithm runs on o n processors in o n time

a look ahead bareiss algorithm for general toeplitz matrices the bareiss algorithm is one of the classical fast solvers for systems of linear equations with toeplitz coefficient matrices the method takes advantage of the special structure and it computes the solution of a toeplitz system of order n with only o n 2 arithmetic operations instead of o n 3 operations however the original bareiss algorithm requires that all leading principal submatrices be nonsingular and the algorithm is numerically unstable if singular or ill conditioned submatrices occur in this paper an extension of the bareiss algorithm to general toeplitz systems is presented using look ahead techniques the proposed algorithm can skip over arbitrary blocks of singular or ill conditioned submatrices and at the same time it still fully exploits the toeplitz structure implementation details and operations counts are given and numerical experiments are reported we also discuss special versions of the proposed look ahead bareiss algorithm for hermitian indefinite toeplitz systems and banded toeplitz systems

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

representation of the drazin inverse for special block matrix abstract for a c n n the matrix x c n n is said to be the drazin inverse of a if it holds that xax x ax xa a r xa a r where r is the smallest nonnegative integer such that rank a r rank a r 1 in this paper we give the representation for the drazin inverse of the block matrix a a b 0 a b c n n a 2 a

the hyberbolic singular value decomposition and applications a new generalization of the singular value decomposition svd the hyperbolic svd is advanced and its existence is established under mild restrictions the hyperbolic svd accurately and efficiently finds the eigenstructure of any matrix that is expressed as the difference of two matrix outer products signal processing applications where this task arises include the covariance differencing algorithm for bearing estimation in sensor arrays sliding rectangular windowing and array calibration two algorithms for effecting this decomposition are detailed one is sequential and follows a similar pattern to the sequential bidiagonal based svd algorithm the other is for parallel implementation and mimics hestenes svd algorithm 1958 numerical examples demonstrate that like its conventional counterpart the hyperbolic svd exhibits superior numerical behavior relative to explicit formation and solution of the normal equations furthermore the hyperbolic svd applies in problems where the conventional svd cannot be employed

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

conjugation interpolation and model matching in h abstract the notion of conjugation is introduced to give a unified framework of algebraic operations connected to the analytic aspects of transfer functions two classes of conjugations are shown to be important one is the lossless conjugation that performs inner outer factorization and the other is the j lossless conjugation that solves the model matching problem related to h 8 control the solution of the model matching problem obtained by j lossless conjugation is regarded as the state space version of the directional interpolation theory and is much simpler than those obtained via the nehari approximation

technical communique global output feedback tracking control for a class of lagrangian systems the problem of global tracking control without velocity measurement of the so called euler lagrange systems has been paid a lot of attention for the past several years in this note a nice property of one degree of freedom euler lagrange systems is highlighted which in particular allows us to obtain a new solution to the problem of tracking control for this class of systems the solution is under the form of a linear like observer based controller which gives fairly good results as illustrated in the simulation the method can be generalized to any system having the same property

inverse scattering and minimal partial realizations we present an inverse scattering interpretation of the classical minimal partial realization problem posed in a slightly generalized context our approach starts by considering a canonical cascade form structure for the realization of arbitrary transfer functions where the cascade structure can be interpreted as the description of a layered wave scattering medium in this context the partial realization problem calls for a recursive process of layer identification from a given input response pair the scattering data the realization algorithm uses a causality principle to progressively determine the parameters of cascaded linear 2 ports that model the successive wave interaction layers this method for approaching the realization problem turns out to fit nicely into a framework that was also used to obtain fast structured linear estimation algorithms and cascade realizations for digital filters

successive matrix squaring algorithm for parallel computing the weighted generalized inverse amn we derive a successive matrix squaring sms algorithm to approximate the weighted generalized inverse which can be expressed in the form of successive squaring of a composite matrix t given an m by n matrix a with m n we show that the weighted generalized inverse of a can be computed in parallel time ranging from o log n to o log 2n provided that there are enough processors to support matrix multiplication in time o log n

explicit group inverse of an innovative patterned matrix in this paper we present an innovative patterned matrix rfpl toeplitz matrix is neither the extension of toeplitz matrix nor its special case we show that the group inverse of this new patterned matrix can be represented as the sum of products of lower and upper triangular toeplitz matrices first the explicit expression of the group inverse of an rfpl toeplitz matrix is obtained second the decomposition of the group inverse is given finally an example demonstrates availability of the two methods for the group inverse

structured matrices and newton s iteration unified approach abstract recent progress in the study of structured matrices shows advantages of unifying the treatment of various classes of such matrices we recall some fundamental techniques for such a unification and then specify it in full details for newton s iteration which rapidly improves an initial approximation to the inverse matrix by performing two matrix multiplications per recursive step the iteration is particularly suitable for n n structured matrices represented with o n entries of their short generators rather than with their own n 2 entries based on such a representation matrix operations are performed much more rapidly and use much less memory space a major problem is to control the length of the generators which tends to grow quite rapidly in the iterative process two known methods solve this problem for toeplitz like and cauchy like matrices we extend both methods to a more general class of structured matrices and estimate the convergence rate as well as the computational complexity some novel techniques are introduced in this study in particular for the estimation of the norms of the inverse displacement operators

on discrete schrodinger equations and their two component wave equation equivalents an approach to inverse scattering problems for discrete schrodinger equations which are discrete three term recursions is presented by systematically transforming them into discrete two component wave propagation equations the wave propagation equations permit the immediate application of certain computationally efficient and physically insightful layer peeling algorithms for inverse scattering the mapping of three term recursions to two component evolution equations is one to many because the relation between the potential sequence parametrizing schrodinger equations and the reflection coefficient sequence determining local wave interaction is a nonlinear difference equation this mapping is examined in some detail and it is used to study both direct and inverse scattering problems associated with discrete schrodinger equations

displacement structure theory and applications in this survey paper we describe how strands of work that are important in two different fields matrix theory and complex function theory have come together in some work on fast computational algorithms for matrices with what we call displacement structure in particular a fast triangularization procedure can be developed for such matrices generalizing in a striking way an algorithm presented by schur 1917 j reine angew math 147 1917 pp 205 232 in a paper on checking when a power series is bounded in the unit disc this factorization algorithm has a surprisingly wide range of significant applications going far beyond numerical linear algebra we mention among others inverse scattering analytic and unconstrained rational interpolation theory digital filter design adaptive filtering and state space least squares estimation

a class of globally convergent velocity observers for robotic manipulators we present a method for global estimation of joint velocities in rigid manipulators a class of velocity observers with smooth dynamics are introduced whose structure depend on freely selectable functions and gains giving the flexibility of achieving multiple design objectives at the same time unlike most methods no a priori knowledge of an upper bound for velocity magnitude is used an adaptive version of the observer is also presented to handle a class of structured uncertainties in manipulator model simulation example illustrates low noise sensitivity of the globally convergent observer in comparison with semi globally convergent observers

further results on iterative methods for computing generalized inverses in this paper we reconsider the iterative method x k x k email protected i ax k 1 k 1 2 email protected email protected 0 for computing the generalized inverse a t s 2 over banach spaces or the generalized drazin inverse a d of a banach algebra element a reveal the intrinsic relationship between the convergence of such iterations and the existence of a t s 2 or a d and present the error bounds of the iterative methods for approximating a t s 2 or a d moreover we deduce some necessary and sufficient conditions for iterative convergence to a t s 2 or a d

higher order convergent iterative method for computing the generalized inverse and its application to toeplitz matrices abstract the main aim of this paper is to provide a higher order convergent iterative method in order to calculate the generalized inverse of a given matrix we extend the iterative method proposed in li et al w g li z li a family of iterative methods for computing the approximate inverse of a square matrix and inner inverse of a non square matrix applied mathematics and computation 215 2010 3433 3442 to compute the 2 inverse generalized inverse a t s 2 2 3 inverse and 2 4 inverse moreover we modify the iterative method to compute the generalized inverse a t s 2 of toeplitz matrices by using the displacement theory

on the statistics of the estimated reflection coefficients of an autoregressive process the exact statistics of the estimated reflection coefficients for an autoregressive process are difficult to determine however since almost all the common methods for estimating the reflection coefficients are maximum likelihood estimates for large data records the asymptotic distribution of the estimates is multivariate gaussian with a covariance matrix given by the cramer rao bound a recursive means of computing the covariance matrix bound is described simulation results show that the asymptotic expressions are accurate for large data records however for relatively short data records the asymptotic expressions are accurate only for spectra with a small dynamic range

new class of control laws for robotic manipulators part 1 non adaptive case a new class of exponentially stabilizing control laws for joint level control of robot arms is introduced it has recently been recognized that the non linear dynamics associated with robotic manip

convergence of newton like methods for singular operator equations using outer inverses we present a semilocal kantorovich type analysis for newton like methods for singular operator equations using outer inverses we establish sharp generalizations of the kantorovich theory and the mysovskii theory for operator equations when the derivative is not necessarily invertible the results reduce in the case of an invertible derivative to well known theorems of kantorovich and mysovskii with no additional assumptions unlike earlier theorems which impose strong conditions the strategy of the analysis is based on banach type lemmas and perturbation bounds for outer inverses which show that the set of outer inverses to a given bounded linear operator admits selections that behave like bounded linear inverses in contrast to inner inverses or generalized inverses which do not depend continuously on perturbations of the operator we give two examples to illustrate our results and compare them with earlier results and another numerical example to relate our results to computational issues

structured mixed and componentwise condition numbers of some structured matrices structured matrices such as cauchy vandermonde toeplitz hankel and circulant matrices are considered in this paper we apply a kronecker product based technique to deduce the structured mixed and componentwise condition numbers for the matrix inversion and for the corresponding linear systems