Confluent Prony approximation
type: Item
instance of: scholarly article
title: Confluent Prony approximation
zbMATH Open document ID: 0754.65012
DOI: 10.1016/0898-1221(91)90189-B
author: Herbert E. Salzer
publication date: 1992-09-27T00:00:00Z
review text: Given \(2n\) data, the interpolating exponential sum \(\sum^ n_{i=1}A_ i\exp(\alpha_ ix)\) is to be determined. If the \(x_ j\)'s are equally spaced, then Prony's classical method may be applied. Typically, first the quantities \(\exp(\alpha_ i h)\) are obtained as the roots of a polynomial of degree \(n\). There is no analogon, if the points are not equally spaced. The author observes that on the other hand the confluent case is easily solved, i.e. the case in which the data are the derivatives at one point. Here the \(\alpha_ i\)'s are obtained from a polynomial equation. The author wonders that this case is not found in textbooks.
reviewed by: D. Braess
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A30
zbMATH DE Number: 60613
zbMATH Keywords: Prony's method
zbMATH Keywords: confluent Prony approximation
zbMATH Keywords: interpolation
zbMATH Keywords: Gaussian quadrature
zbMATH Keywords: Obreschkoff formulae
zbMATH Keywords: exponential sum
MaRDI profile type: Publication
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full work available at URL: 0898-1221(91)90189-b
OpenAlex ID: W2071702245
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 60613