On Row Sequences of Padé and Hermite-Padé Approximation

A survey of direct and inverse type results for row sequences of Padé and Hermite-Padé approximation is given. A conjecture is posed on an inverse type result for type II Hermite-Padé approximation when it is known that the sequence of common denominators of the approximating vector rational functio...

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Bibliographic Details
Published inModern Trends in Constructive Function Theory Vol. 661; pp. 141 - 151
Main Author Simanek, Brian Z
Format Book Chapter
LanguageEnglish
Published Providence, Rhode Island American Mathematical Society 31.03.2016
SeriesContemporary Mathematics
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ISBN1470425343
9781470425340
ISSN0271-4132
1098-3627
DOI10.1090/conm/661/13279

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Summary:A survey of direct and inverse type results for row sequences of Padé and Hermite-Padé approximation is given. A conjecture is posed on an inverse type result for type II Hermite-Padé approximation when it is known that the sequence of common denominators of the approximating vector rational functions has a limit. Some inverse type results are proved for the so called incomplete Padé approximants which may lead to the proof of the conjecture and the connection is discussed.
ISBN:1470425343
9781470425340
ISSN:0271-4132
1098-3627
DOI:10.1090/conm/661/13279