Computation of the singular value expansion
type: Item
instance of: scholarly article
title: Computation of the singular value expansion
zbMATH Open document ID: 0631.65133
DOI: 10.1007/BF02251248
author: Per Christian Hansen
published in: Computing
publication date: 1988-01-01T00:00:00Z
review text: A method for computing the singular values and singular functions of real square-integrable kernels is presented. The analysis shows that a ``good'' discretization always yields a matrix whose singular value decomposition is closely related to the singular value expansion of the kernel. This relationship is important in connection with the solution of ill-posed problems since it shows that regularization of the algebraic problem, derived from an integral equation, is equivalent to the integral equation itself.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45C05
zbMATH DE Number: 4026769
zbMATH Keywords: ill-posed problems
zbMATH Keywords: Fredholm integral equations of the first kind, singular value expansion, singular value decomposition, method of moments, regularization
describes a project that uses: LINPACK
MaRDI profile type: Publication
cites work: The Use of Auto-correlation for Pseudo-rank Determination in Noisy III-conditioned Linear Least-squares Problems
cites work: Q4151113
cites work: Numerical solution of Fredholm integral equations of first kind
cites work: Modifications of some first kind integral equations with logarithmic kernel to improve numerical conditioning
cites work: Q5641599
cites work: Q5185900
cites work: The truncated SVD as a method for regularization
cites work: An SVD analysis of linear algebraic equations derived from first kind integral equations
cites work: A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
cites work: Q3713483
cites work: Numerical Solution of Integral Equations of the First Kind with Nonsmooth Kernels
cites work: Q3251652
cites work: Theory and Methods Related to the Singular-Function Expansion and Landweber’s Iteration for Integral Equations of the First Kind
cites work: Generalizing the Singular Value Decomposition
cites work: A Practical Examination of Some Numerical Methods for Linear Discrete Ill-Posed Problems
cites work: Q3700780
full work available at URL: https://doi.org/10.1007/bf02251248
OpenAlex ID: W2134320246
Recommended article: Computing the Structured Singular Value
Recommended article: Computing the Generalized Singular Value Decomposition
Recommended article: Q3474829
Recommended article: Singular values of matrix exponentials∗
Recommended article: Singular value decomposition in extended double precision arithmetic
Recommended article: Numerical computation of an analytic singular value decomposition of a matrix valued function
Recommended article: Approximating the Generalized Singular Value Expansion
Recommended article: A numerical method for computing the structured singular value
Recommended article: Computing the singular value decomposition with high relative accuracy
description: scientific article; zbMATH DE number 4026769