Abstract
We obtain a closed form expression for the singular values and singular vectors of two matrices arising in the approximation of Cauchy Singular Integral Equations (CSIE) by the Gauss-Chebyshev and Lobatto-Chebyshev quadratures. We also derive their singular value decomposition. We use this decomposition to investigate the convergence of an iterative method for CSIE's, proposed by Ioakimidis (An iterative algorithm for the numerical solution of singular integral equations, J. Computational Physics 43, 164–176 [1981]). We show that this iterative method converges only under very restrictive conditions.
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