Showing papers by "Israel Gohberg published in 1987"
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.
61 citations
TL;DR: In this article, a state space criterion of minimality of a partial realization and a formula for the minimal state space dimension are obtained, and a compression algorithm is constructed which allows one to reduce an arbitrary realization of a finite sequence of matrices M 1, M r to a minimal partial realization of M 1, M r.
46 citations
TL;DR: In this article, a concise account is given of the recent results about inverse spectral problems and minimal divisibility appearing in these three papers, and the present paper serves as an introduction to the papers [BR 2], [BGR] and [GKLR].
Abstract: The present paper serves as an introduction to the papers [BR 2], [BGR] and [GKLR]. For rational matrix functions a concise account is given of the recent results about inverse spectral problems and minimal divisibility appearing in these three papers.
38 citations
TL;DR: In this paper, the authors describe tous les diviseurs minimaux en un point donne d'une fonction matricielle meromorphe in termses de paires spectrales locales and de matrices de couplage locale.
Abstract: Description de tous les diviseurs minimaux en un point donne d'une fonction matricielle meromorphe en termes de paires spectrales locales et de matrice de couplage locale
29 citations
TL;DR: For rational and analytic matrix functions, new formulas for the limits in the Szego-Kac-Achiezer limit theorems were obtained in terms of finite matrices which come from special representations of the matrix functions as discussed by the authors.
23 citations
TL;DR: In this paper, the maximum entropy principle for positive definite extensions of band matrices is generalized to a large class of indefinite self-adjoint matrices, and sufficient conditions are described such that $ | \det F | > | √ √ G |$ when G is any other invertible selfadjoint extension of F.
Abstract: A maximum entropy principle for positive definite extensions of band matrices is generalized here to a large class of indefinite selfadjoint matrices. It is known that a selfadjoint band matrix R with certain nonvanishing minor determinants has a unique extension to an invertible selfadjoint matrix F such that $F^{ - 1} $ is a band matrix. Sufficient conditions are described here such that $ | \det F | > | \det G |$ when G is any other invertible selfadjoint extension of F.
17 citations
TL;DR: In this paper, the simplest representations of triangular parts of finite rank kernels are analyzed and criteria for uniqueness up to similarity are given for minimal realization of systems with separable boundary conditions.
16 citations
TL;DR: In this article, the problem of finding linearly independent vectors x 1,…, x n such that 〈 x k, x j 〉 = a jk for | j − k | ⩽ m and such that the distance from x k to the linear span of x 1,…, X k −1 is maximal for 2 ε, ε ≥ 0.
12 citations
TL;DR: In this paper, a geometrical characterization for the minimal general cascade decomposition of a d-regular rational matrix function defined on a sum of finite-dimensional spaces is given.
Abstract: The paper provides a geometrical characterization for the minimal general cascade decomposition of a d-regular rational matrix function defined on a sum of finite-dimensional spaces. It also contains a necessary and sufficient condition for the stability of such a decomposition, These results, when applied to the case of the linear fractional decompositions of a matrix-valued function lead to a new treatment of the corresponding problems discussed by Helton and Ball (1982) and Gohberg and Rubinstein (1986).
11 citations
10 citations
TL;DR: By noting that a recently introduced class of so-called "diagonal innovation matrices" has a form previously encountered in state-space estimation problems, new linear complexity algorithms are presented for their factorization and inversion.
Abstract: By noting that a recently introduced class of so-called "diagonal innovation matrices" has a form previously encountered in state-space estimation problems, new linear complexity algorithms are presented for their factorization and inversion.
TL;DR: Parallel algorithms with second order precision are derived for efficient numerical solution of Fredholm integral equations of the second kind with displacement kernels.
Abstract: Parallel algorithms with second order precision are derived for efficient numerical solution of Fredholm integral equations of the second kind with displacement kernels.