## Efficient iterative solution of linear systems from discretizing singular integral equations

Ke Chen

### Abstract

In this paper we study the solution of singular integral equations by iterative methods. We show that discretization of singular integral operators obtained by domain splitting yields a system of algebraic equations that has a structure suitable for iterative solution. Numerical examples of Cauchy type singular integral equations are used to illustrate the proposed approach. This paper establishes a theory for experimental results presented previously.

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### Key words

singular integral equations, non-compact operators, direct solutions, preconditioning, conjugate gradient iterative methods.

### AMS subject classifications

65F10, 65N38, 45E05.

### Links to the cited ETNA articles

 [35] Vol. 1 (1993), pp. 11-32 Gerard L. G. Sleijpen and Diederik R. Fokkema: BiCGstab($l$) for linear equations involving unsymmetric matrices with complex spectrum

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