## Abstract Necessary and sufficient conditions for the stability of certain collocation methods applied to Cauchy singular integral equations on an interval are presented for weighted **L**__'__ norms. Moreover, the behavior of the approximation numbers, in particular their soβcalled __k__ βsplitt
Matrix representations associated with collocation methods for Cauchy singular integral equations
β Scribed by P. Junghanns; K. Rost
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 141 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.873
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β¦ Synopsis
Abstract
We prove representations for the coefficient matrices of the linear systems which occur by applying certain collocation methods to Cauchy singular integral equations. These representations use fast discrete trigonometric transforms and give the possibility to design fast algorithms for solving the respective collocation equations. Copyright Β© 2007 John Wiley & Sons, Ltd.
π SIMILAR VOLUMES
The classical polynomial collocation method is considered for a class of Cauchy singular integral equations with variable coefficients on a bounded interval. This method is naturally extended to the case of a non-zero index of the underlying Fredholm operator. This is done by using the structure of
## Abstract In this paper, several boundary element regularization methods, such as iterative, conjugate gradient, Tikhonov regularization and singular value decomposition methods, for solving the Cauchy problem associated to the Helmholtz equation are developed and compared. Regularizing stopping