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Showing papers in "Linear Algebra and its Applications in 1990"


Journal ArticleDOI
TL;DR: In this article, it was shown that reachability and observability indices of appropriately defined pairs of matrices provide the key for solving the minimal rational (bitangen- tial) interpolation problem.

152 citations


Journal ArticleDOI
TL;DR: In this article, the necessary and sufficient conditions for the consistency of linear matrix equations with a symmetric condition on solutions are derived using the singular value decomposition and the generalized singular-value decomposition.

134 citations


Journal ArticleDOI
TL;DR: The separation property that characterizes the dynamics of Markov chains is extended to a class of discrete 2D models where the time support given by the discrete plane Z × Z is partially ordered by the product of the orderings as discussed by the authors.

129 citations


Journal ArticleDOI
TL;DR: In this article, the authors studied the positive (semidefinite) solutions to the matrix equation X = A− BX -1 B ∗ under the assumption that A⩾0.

125 citations


Journal ArticleDOI
TL;DR: In this article, necessary and sufficient conditions are obtained for a pair of matrix equations A1XB1 = C1, A2XB2 = C2 on a general field F to have a common solution, along with the expression for a general common solution when certain conditions hold.

117 citations


Journal ArticleDOI
TL;DR: A fundamental quantity associated with a P-matrix is introduced and it is shown how this quantity is useful in deriving error bounds for the linear complementarity problem of the P-type.

105 citations


Journal ArticleDOI
TL;DR: In this article, the convergence and regularization properties of SIRT and CG-type methods for least-squares problems arising in tomography were compared and it was shown that virtually the same solutions as obtained by SIRT methods can be obtained by applying a CG-based method to a properly rescaled system, but with an amount of work proportional to the square root of the amount of SIR with SIRT.

105 citations


Journal ArticleDOI
TL;DR: It is shown that if the matrices P 1,…, P n are paracontracting in the same smooth, strictly convex norm and if the sequence j i ∞ i = 1 has certain regularity properties, then the above iterates converge.

94 citations


Journal ArticleDOI
TL;DR: Study of multiplicative iterative algorithms for the minimization of a differentiable, convex function defined on the positive orthant of R N and the convergence is nearly monotone in the sense of Kullback-Leibler divergence.

87 citations


Journal ArticleDOI
TL;DR: In this article, the problem of passing from interpolation data for a real rational transfer-function matrix to a minimal state-variable realization of the transfer function matrix is considered, where the tool is a Loewner matrix, which is a generalization of the Standard Hankel matrix of linear system realization theory and possesses a decomposition into a product of generalized observability and controllability matrices.

85 citations



Journal ArticleDOI
TL;DR: A new randomized parallel algorithm that determines the Smith normal form of a matrix with entries being univariate polynomials with coefficients in an arbitrary field that is probabilistic of Las Vegas type and reduces the problem of Smith form computation to two Hermite form computations.

Journal ArticleDOI
TL;DR: In this article, the authors give an interpretation of the limit in terms of a generalized inverse of A and derive bounds with respect to the least-squares solution, using a result of Buoni and Varga.

Journal ArticleDOI
TL;DR: In this paper, it was shown that if the integral domain is a principal ideal domain, every generalized inverse can be obtained by that procedure, and it was also shown that a matrix A of rank r over an integral domain has Moore-Penrose inverse if and only if the sum of squares of all r × r minors of A is an invertible element of the integral domains.

Journal ArticleDOI
TL;DR: In this article, it was shown that under mild conditions the minimizers in (1) are essentially unique and are related to the left and right singular vectors of A in a simple way.

Journal ArticleDOI
TL;DR: In this paper, a quasilinear representation for unitarily invariant norms is proposed, and a basic inequality of the Cauchy-schwarz type is proved.

Journal ArticleDOI
Ji-guang Sun1
TL;DR: In this paper, the authors survey the development of sensitivity analysis of multiple eigenvalues and the associated invariant subspaces of two kinds of matrix eigenvalue problems, in which the matrices are analytically dependent on several parameters.

Journal ArticleDOI
TL;DR: In this paper, the generalized Bott-Duffin inverse A (+) (L ) of A with respect to a subspace L is defined, and a unified treatment of a class of linear systems and extreme value problems with equality constraints is given.

Journal ArticleDOI
TL;DR: In this paper, it was shown that for Hilbert space operators, with S invertible hermitian, it is shown that ⇁STS -1 + S -1 TS⇁⩾2�ↆT�T ↆ T + TS↓↘ T↩ 2↔ T + T

Journal ArticleDOI
TL;DR: In this article, the authors examined the extreme points of R n focusing mainly on their rank and showed that R n contains extreme points with rank k if and only if k (k + 1)⩽2 n.

Journal ArticleDOI
TL;DR: In this paper, an explicit determinantal formula for the least square solution of an over-determined system of linear equations was derived, and it was shown that the least squares solution lies in the convex hull of the solutions to the square subsystems of the original system.

Journal ArticleDOI
TL;DR: In this paper, the symmetric Lanczos algorithm and subspace iteration are used to compute some eigenpairs of the linear quadratic eigenvalue problem with symmetric positive definite coefficient matrices, but neither of them will be positive definite.

Journal ArticleDOI
P. Van Dooren1
TL;DR: In this article, a recursive algorithm for obtaining factorizations of the type ======R(λ)=R1(λ)R2(λ), where all three matrices are rational and R 1 (λ) is nonsingular, is presented.

Journal ArticleDOI
TL;DR: In this paper, the distance between the roots of two polynomials in terms of their coefficients and the distances between the eigenvalues of two matrices in the norm of their difference were derived.


Journal ArticleDOI
TL;DR: In this paper, the authors consider the group GL n A of all invertible n by n matrices over a ring A satisfying the first Bass stable range condition and prove that every matrix is similar to the product of a lower and upper triangular matrix.

Journal ArticleDOI
TL;DR: In this article, it was shown that the matrix representations of the basis elements of a Clifford algebra can be chosen to satisfy a certain additional trace condition; then, this trace condition was used to establish optimal inequalities involving norms in Clifford algebras.

Journal ArticleDOI
TL;DR: In this paper, it was shown that αK+ Z 2 = R 2 for α⩾1+ 2 3 √3, and that this bound is best possible.

Journal ArticleDOI
TL;DR: The solvable Lie algebras of dimension not greater than four over a perfect field of reference are described in terms of their nilpotent frame, counted over finite fields of q elements, and classified over real and complex number fields as mentioned in this paper.

Journal ArticleDOI
TL;DR: A new mathematical state-space model for a class of nonlinear time-varying parallel iterative schemes is proposed, and it is shown that the well-known quasidominance condition on a certain aggregated matrix guarantees exponential convergence of this class of methods.