Interpolation by a sum of exponential functions when some exponents are preassigned
type: Item
instance of: scholarly article
title: Interpolation by a sum of exponential functions when some exponents are preassigned
zbMATH Open document ID: 0592.41002
DOI: 10.1016/0022-247X(85)90282-3
author: Avram Sidi
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: Recently [J. Approximation Theory 34, 194-210 (1982)] the author has solved two interpolation problems. The first one is for equidistant nodes and the other for confluent nodes and in each case interpolation is by a sum of exponential functions where none of the exponents are known. Necessary and sufficient conditions for the existence and uniqueness of their solutions and explicit formulae were given in terms of the corresponding Padé approximants. Here the author generalizes these results by specifying some of the exponents. Again he obtains necessary and sufficient conditions for existence and uniqueness of the solutions and also gives the explicit form of the solutions when some of the exponents are known. Using the connection with Padé approximation, he also proves that under certain conditions, the discrete case converges to the confluent case.
reviewed by: A. Sharma
Mathematics Subject Classification ID: 41A05
zbMATH DE Number: 3951187
zbMATH Keywords: interpolation problems
zbMATH Keywords: exponential functions
zbMATH Keywords: Padé approximants
zbMATH Keywords: Padé approximation
MaRDI profile type: Publication
cites work: Q4076249
cites work: Q5678345
cites work: Q4057549
full work available at URL: 0022-247x(85)90282-3
OpenAlex ID: W1996717203
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description: scientific article; zbMATH DE number 3951187