Generalized Inverses in Numerical Solutions of Cauchy Singular Integral Equations
Commun. Korean Math. Soc. 1998 Vol. 13, No. 4, 875-888
S. Kim
Ewha Womans University
Abstract : The use of the zeros of Chebyshev polynomial of the first kind $T_{4n+4}(x)$ and second kind $U_{2n+1}(x)$ for Gauss-Chebyshev quadrature and collocation of singular integral equations of Cauchy type yields computationally accurate solutions over other combinations of $T_n(x)$ and $U_{m}(x)$ as in \cite{skim}. We show that the coefficient matrix of the overdetermined system %from $T_{4n+4}(x)$ and $U_{2n+1}(x)$ has the generalized inverse. We estimate the residual error using the norm of the generalized inverse.
Keywords : generalized inverses, numerical solutions of integral equations
MSC numbers : 65
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