SOLVING SINGULAR INTEGRAL-EQUATIONS USING GAUSSIAN QUADRATURE AND OVERDETERMINED SYSTEM

Gauss-Chebyshev quadrature and collocation at the zeros of the Chebysh ev polynomial of the first kind T-n(x), and second kind U-n(x) leads t o an overdetermined system of linear algebraic equations. The size of the coefficient matrix for the overdetermined system-depends on the de grees of Chebyshev polynomials used. We show that we can get more accu rate solution using T4n+4(x), than other T-n(x). The regularization me thod using Generalized Singular Value Decomposition is described and c ompared to Gauss-Newton method for solving the overdetermined system o f equations. Computational tests show that GSVD with an appropriate ch oice of regularization parameter gives better solution in solving sing ular integral equations. (C) 1998 Elsevier Science Ltd. All rights res erved.