Numerical solution of positive sum exponential equations
type: Item
instance of: scholarly article
title: Numerical solution of positive sum exponential equations
zbMATH Open document ID: 0685.65047
DOI: 10.1016/0096-3003(89)90008-8
author: K. Appert
published in: Applied Mathematics and Computation
publication date: 1989-01-01T00:00:00Z
review text: Let \(F: {\mathbb{R}}^ n\to {\mathbb{R}}^ n\) be a differentiable mapping. In principle, the trajectory of the initial value problem \(F'(x)dx/dt=- F(a),\quad x(0)=a\) provides the solution of \(F(x)=0\) at \(t=1.\) This continuous version of Newton's method is discussed in the first paper. In the second one it is applied to Prony's method for the interpolation of 2n equidistant data by sums of exponentials. The authors observe that the inherent instability of the method (problem?) cannot be overcome by the continuation method.
reviewed by: D. Braess
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 11L03
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A30
zbMATH DE Number: 4123177
zbMATH Keywords: positive sum exponential equations
zbMATH Keywords: homotopy continuation method
zbMATH Keywords: inverse interpolation problem
zbMATH Keywords: Prony's method
zbMATH Keywords: sums of exponentials
zbMATH Keywords: instability
describes a project that uses: minpack
describes a project that uses: HOMPACK
MaRDI profile type: Publication
full work available at URL: 0096-3003(89)90008-8
OpenAlex ID: W1991719121
cites work: On Least Squares Exponential Sum Approximation With Positive Coefficients
cites work: Parameter identification by continuation methods
cites work: Finding roots of equations in given neighborhoods
cites work: Fitting Empirical Data by Positive Sums of Exponentials
cites work: Q4117285
cites work: Algorithm 652
description: scientific article; zbMATH DE number 4123177