Showing papers in "Linear Algebra and its Applications in 1987"
TL;DR: An algorithm is presented for computing a column permutation Pi and a QR-factorization of an m by n (m or = n) matrix A such that a possible rank deficiency of A will be revealed in the triangular factor R having a small lower right block.
525 citations
TL;DR: A concise survey on totally positive matrices and related topics can be found in this paper, where the authors present a unified method for computing the total positivity of a matrices.
443 citations
TL;DR: In this article, the matrix-sign-function algorithm for algebraic Riccati equations is improved by a simple reorganization that changes nonsymmetric matrix inversions into symmetric matrix inverse inversions.
212 citations
TL;DR: An extension of the Schur method is presented which enables real arithmetic to be used throughout when computing a real square root of a real matrix.
208 citations
TL;DR: In this paper, it is shown how to obtain a best approximation of lower rank in which a specified set of columns of the matrix remains fixed, and some applications of the generalization are discussed.
197 citations
TL;DR: In certain cases the rate of global convergence of these parallel iterative methods is inherent in the splitting of A and is independent of the manner in which the work is distributed among the processors, so in general one can distribute the work for load balancing purposes without affecting the convergence rate.
176 citations
TL;DR: The spectral radius p(A) of the adjacency matrix A of a graph G with e edges satisfies p (A)
143 citations
TL;DR: The recurrences used are closely related to the Zohar-Trench and Bareiss algorithms but do not have any obvious connection with other asymptotically fast algorithms for the inversion of Toeplitz systems.
116 citations
TL;DR: In this paper, the stability of algorithms in numerical linear algebra is discussed and the concept of stability is extended to notions of weak stability and strong stability, and the implications of error analyses in terms of these definitions are discussed.
115 citations
TL;DR: The conditions for the existence of a unique solution of the matrix equation AXB−CXD=E are proved in this article, and a numerical algorithm for solving the equation is proposed.
112 citations
TL;DR: In this article, the existence of an n × n matrix over an arbitrary field when its invariant polynomials and either some rows or columns are prescribed is solved in terms of invariant factor inequalities and of majorization inequalities involving controllability indices and the degrees of the invariants.
TL;DR: In this article, the controllability and reachability of discrete linear control systems with nonnegative entries have been studied, and the authors show that the reachability is not equivalent to controllable systems.
TL;DR: In this paper, necessary and sufficient conditions for the consistency of the linear matrix equations are derived, some using the generalized singular value decomposition, and Numerical algorithms for the solutions are also suggested.
TL;DR: In this article, it was shown that if the initial iteration matrix is nonnegative, then Gauss-Seidel iteration matrix can improve the convergence rate of the original linear system.
TL;DR: In this paper, the real space of all real symmetric or complex self-adjoint matrices is characterized for adjoint-preserving maps on all n × n matrices.
TL;DR: In this paper, the group inverse of a matrix is used to define the #-order on square matrices of index 1, which is similar to the ∗-order of Drazin [2] and the minus order of Hartwig [6, 10] and Nambooripad [17].
TL;DR: In this article, a partitioned minimum-norm reflexive generalized inverse is applied to find the general symmetric solution X to the matrix equation AX=B and the dimension of the space of symmetric solutions is established.
TL;DR: A survey of general properties of the cone of positive semidefinite matrices, its faces, two isometric isomorphisms, and linear transformations on it is given in this paper.
TL;DR: In this article, the authors examined several approaches and discussed their respective merits under various circumstances and concluded that complex arithmetic can be avoided only at the expense of losing the advantage of bandedness of the pair.
TL;DR: In this article, it was shown that a sufficient condition for a nonnegative real symmetric matrix to be completely positive is that the matrix is diagonally dominant (i.e., the dominant matrix is diagonal).
TL;DR: It is shown that by adding a correction step using only single precision the authors get a method which under mild conditions is as accurate as the QR method.
TL;DR: A method of derivation of parallel algorithms for ( N + 1) × ( N − 1) matrices with recursive structure is presented and applied to Toeplitz, Hankel, and other ToEplitz-like matrices.
TL;DR: In this paper, the convergence behavior of Ritz values corresponding to a pair of close eigenvalues in the spectrum has been studied and the local effects that are typical for such a situation are illustrated by numerical examples.
TL;DR: Han and Robinson as mentioned in this paper showed that the equivalence of strong stability in the sense of M. Kojima and strong regularity under a regularity assumption is true without any regularity assumptions.
TL;DR: In this paper, the location of eigenvalues for diagonally dominant infinite matrices is investigated, and upper and lower bounds for eigen values are established for tridiagonal matrices.
TL;DR: In this article, a sufficient condition for complete positivity of a matrix, in terms of complete positive of smaller matrices, is given and the patterns for which this condition is also necessary are characterized.
TL;DR: In this article, several measures of nonnormality of matrices are discussed, i.e., functions v: Cn, n → R plus where v(A)=0 iff A is normal.
TL;DR: A more general definition of block H-matrices is introduced and the theory of existence and applicability of these factorizations is extended to this class of matrices.
TL;DR: In this paper, a finitely computable graph-theoretic answer is given to the following question concerning linear dynamical systems: When, given only the signs of entries (+, -, or 0) in a real square matrix A, can one be certain that all positive trajectories of the system ẋ = Ax are bounded?
CSAV1
TL;DR: In this article, an infinite locally finite graph such that its adjacency operator is not self-adjoint is shown. But this is not a negative answer to a conjecture of Mohar.