Rectangular matrix Padé approximants and square matrix orthogonal polynomials

In this paper we study Padé-type and Padé approximants for rectangular matrix formal power series, as well as the formal orthogonal polynomials which are a consequence of the definition of these matrix Padé approximants. Recurrence relations are given along a diagonal or two adjacent diagonals of th...

Full description

Saved in:
Bibliographic Details
Published inNumerical algorithms Vol. 14; no. 4; pp. 321 - 341
Main Authors Draux, André, Moalla, Borhane
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.01.1997
Subjects
Algorithms
Polynomials
Power series
Online AccessGet full text

Cover

More Information
Summary:In this paper we study Padé-type and Padé approximants for rectangular matrix formal power series, as well as the formal orthogonal polynomials which are a consequence of the definition of these matrix Padé approximants. Recurrence relations are given along a diagonal or two adjacent diagonals of the table of orthogonal polynomials and their adjacent ones. A matrix qd-algorithm is deduced from these relations. Recurrence relations are also proved for the associated polynomials. Finally a short presentation of right matrix Padé approximants gives a link between the degrees of orthogonal polynomials in right and left matrix Padé approximants in order to show that the latter are identical.
ISSN:1017-1398
1572-9265
DOI:10.1023/A:1019177316794