Solving singular integral equations using Gaussian quadrature and overdetermined system

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Gauss-Chebyshev quadrature and collocation at the zeros of the Chebyshev polynomial of the first kind Tn(x), and second kind Un(x) leads to an overdetermined system of linear algebraic equations. The size of the coefficient matrix for the overdetermined system depends on the degrees of Chebyshev polynomials used. We show that we can get more accurate solution using T4n+4(x), than other Tn(x). The regularization method using Generalized Singular Value Decomposition is described and compared to Gauss-Newton method for solving the overdetermined system of equations. Computational tests show that GSVD with an appropriate choice of regularization parameter gives better solution in solving singular integral equations.

Original languageEnglish
Pages (from-to)63-71
Number of pages9
JournalComputers and Mathematics with Applications
Issue number10
StatePublished - May 1998

Bibliographical note

Funding Information:
Research supported by Korean Ministry of Education, BSRI-97-1430 and Ewha Women's University, 1996. The author wishes to thank R. P. Tewarson for his hospitality during the author's visit to SUNY Stony Brook and R. P. Srivastav for his helpful comments.


  • Gauss-Chebyshev quadrature
  • Generalized singular
  • Overdetermined systems
  • Tikhonov regularization
  • Value decomposition


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