Showing papers in "Linear Algebra and its Applications in 1993"

TL;DR: In this article, the authors consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices, each of which depends affinely on the decision variables.

TL;DR: The nonnegative rank of a nonnegative matrix is the smallest number of non negative rank-one matrices into which the matrix can be decomposed additively.

TL;DR: In this article, a study is made of the extreme points of the convex set of doubly stochastic completely positive maps of the matrix algebra M n and a tilde operation is defined on the linear maps of M n to give an elementary derivation of a result of Kummerer and Maassen.

TL;DR: In this article, the authors considered the problem of finding a positive definite solution of the matrix equation X + A ∗ X -1 A = Q in a special case of the discrete-time Riccati equation.

TL;DR: In this article, the question under which conditions on the real (square) matrix A the matrix equation X+ATX−1A=I has a real symmetric positive definite solution X is raised.

TL;DR: In this article, it is shown how structured and weighted total least squares and L 2 approximation problems lead to a nonlinear generalized singular value decomposition, and an inverse iteration scheme to find a (local) minimum is proposed.

TL;DR: In this paper, a class of trace inequalities which complements the Golden-Thompson inequality was shown to hold for all p > 0 when A and B are Hermitian matrices and # denotes the geometric mean.

TL;DR: In this article, the authors discuss another tool to analyze the behavior of an iterative method, namely the field of values W (T ), the collection of all Rayleigh quotients of T.

TL;DR: In this article, a characterization of additive mappings on the subalgebra of all finite-rank operators which preserve operators of rank one or projections of rank two is given. In the real case such mappings are automatically linear.

TL;DR: A new version of an existing algorithm for reordering the eigenvalues on the diagonal of a matrix in real Schur form by performing an orthogonal similarity transformation is discussed.

TL;DR: In this article, the authors derive algorithms for the iterative reconstruction of discrete band-limited signals from their irregular samples at a geometric rate, and all constants are computable explicitly.

TL;DR: In this paper, the authors present several solvability concepts for linear differential-algebraic equations (DAEs) with constant coefficients on the positive time axis as well as for the associated singular systems, and investigate under which conditions these concepts are met.

TL;DR: In this article, it was shown that for any m × n column-stochastic matrix A, the contraction coefficient defined as ηg(A) = sup{Hg(Ax,Ay)/hg(x,y) : x,y ∈ Pn, x ≠ y} satisfies η g(A ⩽1 - α(A), where α(a) = minj,kΣi min(aij, aik) is Dobrushin's coefficient of ergodicity.

TL;DR: Some properties of a particular positive definite Toeplitz matrix of arbitrary order, which is called the prolate matrix, arises naturally in signal processing, and it is extremely ill conditioned.

TL;DR: In this article, the authors obtained Furuta's inequality under chaotic order for positive invertible operators A and B, and applied it to a generalization of Ando's theorem.

TL;DR: In this article, an iterative algorithm for moving a triangular matrix toward diagonality was proposed, which is related to algorithms for refining rank-revealing triangular decompositions and in a variant form, to the QR algorithm.

TL;DR: The Lanczos algorithm is used, modified in two ways, to solve large sparse systems of linear equations over GF(2), the field with two elements, and has much lower space requirements than structured Gaussian elimination.

TL;DR: In this article, an inversion formula is presented, and fast solution algorithms with O(n log 2 n) complexity for Cauchy-Vandermonde systems are developed.

TL;DR: The algorithm is intended to compute the projection matrices P and I - P onto the deflating subspaces of matrix pencils corresponding to the eigenvalues inside and outside the unit circle to solve the Riccati equation.

TL;DR: In this article, the perturbation properties of the eigensolution of Hermitian matrices were studied and a new class of well-behaved matrices and matrix pairs were obtained.

TL;DR: This work proposes a new type of preconditioners for Hermitian positive definite Toeplitz systems A n x = b where A n are assumed to be generated by functions f that are positive and 2π-periodic and proves that any ToePlitz matrix can be written as a sum of { ω }-circulant matrices.

TL;DR: In this article, a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one.

TL;DR: The recently developed algorithm of Niederreiter for the factorization of polynomials over finite fields provides a “linearization” of the factorsization problem via differential equations in rational function fields.

TL;DR: In this article, the authors provide definitions and conditions for two notions of left (right) invertibility of a general singular system in terms of their distributions, subspaces, and Rosenbrock's system matrix.

TL;DR: In this article, necessary and sufficient conditions for the existence of the stabilizing solution of the algebraic Riccati equation were derived for both the continuous and the discrete-time case under the weakest possible assumptions imposed on the initial data.

TL;DR: Two nonmodal algorithms are described, and it is shown mathematically that under some mild assumptions on the damping matrix, the feedback matrix obtained by each algorithm indeed stabilizes a closed-loop system.

TL;DR: In this paper, the sharp Lipschitz constants for the feasible solutions and optimal solutions of a linear program with respect to right-hand-side perturbations are derived in terms of pseudoinverses of submatrices of the matrices involved.

TL;DR: Criteria to guarantee the feasibility and the optimality of the Cholesky method to bound the solutions of linear systems with symmetric matrices and right-hand sides both of which are varying within given intervals is derived.

TL;DR: In this article, the authors considered the question of whether a real partial positive definite matrix (in which the specified off-diagonal entries consist of a full n-cycle) has a positive definite completion.

TL;DR: In this paper, the authors give a description of derivations in Tn(R), the ring of upper triangular matrices over a ring R, assuming only the existence of an identity element.