The use of Sherman-Morrison formula in the solution of Fredholm integral equation of second kind
type: Item
instance of: scholarly article
title: The use of Sherman-Morrison formula in the solution of Fredholm integral equation of second kind
zbMATH Open document ID: 1209.65144
author: P. Maponi
author: N. Egidi
published in: Mathematics and Computers in Simulation
publication date: 2011-01-31T00:00:00Z
review text: A constructive method for the solution of Fredholm integral equations of the second kind is provided. This method is based on a simple generalization of the Sherman-Morrison formula for matrices to corresponding operators in infinite-dimensional spaces. In particular, this method is recursive and delivers a sequence of functions converging to the exact solution of the integral equation. The convergence result is proved for the case of Fredholm integral equations with square integrable kernels. The results are applied to a boundary value problem for the Laplace operator. Several variants of the employed method are suggested.
reviewed by: Ludwig Kohaupt
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N38
zbMATH DE Number: 5843137
zbMATH Keywords: Sherman-Morrison formula
zbMATH Keywords: Fredholm integral equation of second kind
zbMATH Keywords: constructive method
zbMATH Keywords: recursive method
zbMATH Keywords: boundary value problem
zbMATH Keywords: potential theory for Laplace operator
zbMATH Keywords: convergence
MaRDI profile type: Publication
full work available at URL: j.matcom.2010.03.006
OpenAlex ID: W2077988574
Wikidata QID: Q124542257
cites work: The Numerical Solution of Fredholm integral Equations of the Second Kind
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cites work: Linear integral equations
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cites work: Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix
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cites work: Q5638625
DOI: 10.1016/J.MATCOM.2010.03.006
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description: scientific article; zbMATH DE number 5843137