The Extended Euclidean algorithm for matrix Padé approximants is applied to compute matrix Padé approximants when the coefficient matrices of the input matrix polynomial are triangular. The procedure given by Bjarne S. Anderson et al. for packing a triangular matrix in recursive packed storage is applied to pack a sequence of lower triangular matrices of a matrix polynomial in recursive packed storage. This recursive packed storage for a matrix polynomial is applied to compute matrix Padé approximants of the matrix polynomial using the Matrix Padé Extended Euclidean algorithm in packed form. The CPU time and memory comparison, in computing the matrix Padé approximants of a matrix polynomial, between the packed case and the non-packed case are described in detail. © 2009 Elsevier Ltd. All rights reserved.

S. Sundar

Department of Mathematics

Polynomials

ANDERSONS

APPROXIMANTS

Coefficient matrix

EXTENDED EUCLIDEAN ALGORITHM

Input matrices

Matrix polynomials

Recursive formulation

TRIANGULAR MATRICES

Matrix algebra

Fulltext

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Computers and Mathematics with Applications

Work on Padé or Padé-type approximants ultimately involves the explicitdetermination of the polynomials forming the numerator and denominator of rational functions. These exist in the literature useful algorithms for constructing the polynomials when the starting coefficients of the given power series are of the ordinary kind. However, when one has the matrix coefficients forthe series, it becomes necessary to extend the procedure taking into account the special nature of the various operations. In this paper we present a new application of the extended Euclidean algorithm in order to obtain the sets of complete matrix Padé approximants. Also, an efficient Pascal procedure for implementation of the algorithm is given. In fact, the resulting algorithm generates the elements in the anti-diagonal of the Padé table. The concepts and constructive steps involved in the procedure are explained in detail and illustrated by a few suitable examples to show (i) how the algorithm works in general and (ii) the usefulness of the entire approach. © 1988.

A new application of the extended Euclidean algorithm for matrix padé approximants

Numerical Methods for Engineers and Scientists Using MATLAB®, Second Edition

ACM Transactions on Mathematical Software (TOMS)

A recursive formulation of Cholesky factorization of a matrix in packed storage

Mathematics of Computation

Recursive algorithms for the matrix Padé problem

Journal of Algorithms

Fast solution of toeplitz systems of equations and computation of Padé approximants

Recursive formulation of the matrix Padé approximation in packed storage

Journal	Data powered by TypesetComputers and Mathematics with Applications
Publisher	Data powered by TypesetElsevier Ltd
ISSN	08981221
Open Access	Yes