Quadrature Methods for Strongly Elliptic Cauchy Singular Integral Equations on an Interval

This paper is concerned with a quadrature method for singular integral equations on a finite interval. It is proved that the strong ellipticity is necessary and sufficient for this numerical procedure to be stable. The proof of this result is based on the symbol calculus on the algebra generated by Toeplitz matrices due to Gohberg and Krupnik [12].Estimates for the speed of convergence as well as numerical examples are given.

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