The fit of a sum of exponentials to noisy data
type: Item
instance of: scholarly article
title: The fit of a sum of exponentials to noisy data
zbMATH Open document ID: 0644.65010
DOI: 10.1016/0377-0427(87)90135-X
author: B. De Moor
author: P. P. N. de Groen
published in: Journal of Computational and Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The approximation by sums of exponentials is studied in a system theoretic framework. Let data \(y_ i\) are given at equidistant points. The Hankel matrices \((y_{i+j-1})\) and \((y_{i+j})\) are factorized into an observability matrix and a controllability matrix. The system matrix can be determined from them. The influence of noice is considered. For its analysis error estimates for the singular value decompositions are derived and applied.
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 11T23
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93B07
zbMATH DE Number: 4050842
zbMATH Keywords: fitting
zbMATH Keywords: approximation by sums of exponentials
zbMATH Keywords: Hankel matrices
zbMATH Keywords: observability matrix
zbMATH Keywords: controllability matrix
zbMATH Keywords: influence of noice
zbMATH Keywords: error estimates
zbMATH Keywords: singular value decompositions
reviewed by: D. Braess
MaRDI profile type: Publication
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full work available at URL: 0377-0427(87)90135-x
OpenAlex ID: W2001957929
description: scientific article; zbMATH DE number 4050842