The use of Sherman-Morrison formula in the solution of Fredholm integral equation of second kind (Q622201)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The use of Sherman-Morrison formula in the solution of Fredholm integral equation of second kind |
scientific article; zbMATH DE number 5843137
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The use of Sherman-Morrison formula in the solution of Fredholm integral equation of second kind |
scientific article; zbMATH DE number 5843137 |
Statements
The use of Sherman-Morrison formula in the solution of Fredholm integral equation of second kind (English)
0 references
31 January 2011
0 references
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.
0 references
Sherman-Morrison formula
0 references
Fredholm integral equation of second kind
0 references
constructive method
0 references
recursive method
0 references
boundary value problem
0 references
potential theory for Laplace operator
0 references
convergence
0 references
0 references
0 references
0 references
0.86550146
0 references
0.86442316
0 references
0.86111546
0 references
0.8608818
0 references
0 references
0.8590987
0 references
