Volume 16, Issue 5
Probabilistic Analysis of Galerkin-Like Methods for the Fredholm Equation of the Second Kind
DOI:

J. Comp. Math., 16 (1998), pp. 445-456

Published online: 1998-10

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• Abstract

This paper deals with the approximate solution of the Fredholm equation $u-T_Ku=f$ of the second kind from a probabilistic point of view. With Wiener type measures on the set of kernels and free terms we determine statistical features of the approximation process, i.e., the most likely rate of convergence and the dominating individual behavior. The analysis carried out for a kind of Galerkin-like method.

• Keywords

Probabilistic analysis fredholm equation galerkin-like method abstract wiener space

@Article{JCM-16-445, author = {}, title = {Probabilistic Analysis of Galerkin-Like Methods for the Fredholm Equation of the Second Kind}, journal = {Journal of Computational Mathematics}, year = {1998}, volume = {16}, number = {5}, pages = {445--456}, abstract = { This paper deals with the approximate solution of the Fredholm equation $u-T_Ku=f$ of the second kind from a probabilistic point of view. With Wiener type measures on the set of kernels and free terms we determine statistical features of the approximation process, i.e., the most likely rate of convergence and the dominating individual behavior. The analysis carried out for a kind of Galerkin-like method. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9174.html} }
TY - JOUR T1 - Probabilistic Analysis of Galerkin-Like Methods for the Fredholm Equation of the Second Kind JO - Journal of Computational Mathematics VL - 5 SP - 445 EP - 456 PY - 1998 DA - 1998/10 SN - 16 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9174.html KW - Probabilistic analysis KW - fredholm equation KW - galerkin-like method KW - abstract wiener space AB - This paper deals with the approximate solution of the Fredholm equation $u-T_Ku=f$ of the second kind from a probabilistic point of view. With Wiener type measures on the set of kernels and free terms we determine statistical features of the approximation process, i.e., the most likely rate of convergence and the dominating individual behavior. The analysis carried out for a kind of Galerkin-like method.