Generalized inverse matrix Padé approximation on the basis of scalar products
type: Item
instance of: scholarly article
title: Generalized inverse matrix Padé approximation on the basis of scalar products
zbMATH Open document ID: 0967.15004
DOI: 10.1016/S0024-3795(00)00230-5
author: Chuanqing Gu
published in: Linear Algebra and its Applications
publication date: 2001-09-03T00:00:00Z
review text: An axiomatic definition to matrix Padé approximants is presented as an extension of that by \textit{P. R. Graves-Morris} and \textit{C. D. Jenkins} [Constructive Approximation 2, 263-289 (1986; Zbl 0614.41010)]. The expression for this approximant has a matrix numerator and a scalar denominator. It does not need any multiplication of matrices. The representations of this approximant type are provided with three forms: (i) by explicit determinantal formulas for the denominator scalar polynomials and the numerator matrix polynomials, (ii) by an \(\varepsilon\)-algorithm, and (iii) by Thiele-type continued fraction. Equivalence relations for the three representations are proposed.
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 1559346
zbMATH Keywords: generalized inverse
zbMATH Keywords: matrix Padé approximation
zbMATH Keywords: epsilon algorithm
zbMATH Keywords: Thiele-type continued fraction
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1559346