Solving singular integral equations using Gaussian quadrature and overdetermined system

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

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
Volume35
Issue number10
DOIs
StatePublished - May 1998

Keywords

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

Fingerprint

Dive into the research topics of 'Solving singular integral equations using Gaussian quadrature and overdetermined system'. Together they form a unique fingerprint.

Cite this