Interpretation and solution of ill-conditioned equations arising in parameter estimation and system identification
type: Item
instance of: scholarly article
title: Interpretation and solution of ill-conditioned equations arising in parameter estimation and system identification
zbMATH Open document ID: 0731.93021
DOI: 10.1016/0895-7177(90)90177-O
author: Irving U. Ojalvo
published in: Mathematical and Computer Modelling
publication date: 1990-01-01T00:00:00Z
review text: A new method, named Epsilon Decomposition (E-D), for the efficient solution of ill-conditioned linear algebraic equations is presented. It represents a significant improvement over Singular Value Decomposition (SVD), which requires the user to obtain all the eigenvalues and eigenvectors of all ill-conditioned matrix. This can be quite costly if the matrix is large. The efficiency associated with E-D resides in the fact that the user need only obtain the zero, near-zero and the lowest non-zero eigenvalues of the coefficient matrix of the system of equations. The equivalence of E-D and SVD is based upon the fact that E-D produces a very small, \(\epsilon\), shift in the non-zero and near-zero eigenvalues without any need to compute them. The mathematical interpretation of the E-D and SVD solutions is that they produce the same minimum norm solutions. A numerical example is presented in detail.
Mathematics Subject Classification ID: 93B30
Mathematics Subject Classification ID: 65F05
zbMATH DE Number: 4209967
zbMATH Keywords: Epsilon Decomposition
zbMATH Keywords: ill-conditioned linear algebraic equations
zbMATH Keywords: Singular Value Decomposition
zbMATH Keywords: numerical example
reviewed by: Yousri M. El-Fattah
MaRDI profile type: Publication
cites work: Four algorithms for the the efficient computation of truncated pivoted QR approximations to a sparse matrix
full work available at URL: 0895-7177(90)90177-o
OpenAlex ID: W2090201942
description: scientific article; zbMATH DE number 4209967