TY - JOUR

T1 - Solving singular integral equations using Gaussian quadrature and overdetermined system

AU - Kim, S.

N1 - 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.

PY - 1998/5

Y1 - 1998/5

N2 - 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.

AB - 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.

KW - Gauss-Chebyshev quadrature

KW - Generalized singular

KW - Overdetermined systems

KW - Tikhonov regularization

KW - Value decomposition

UR - http://www.scopus.com/inward/record.url?scp=0032067907&partnerID=8YFLogxK

U2 - 10.1016/S0898-1221(98)00073-X

DO - 10.1016/S0898-1221(98)00073-X

M3 - Article

AN - SCOPUS:0032067907

SN - 0898-1221

VL - 35

SP - 63

EP - 71

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 10

ER -