论文信息 - Asymptotic stability of the fundamental solution method

Asymptotic stability of the fundamental solution method

Abstract In a previous paper (1988) we studied the numerical stability of the fundamental solution method applied to the Dirichlet problem of Laplace's equation, and presented a practical scheme for examining the stability of the method using the singular value decomposition. In the present paper, we give an asymptotic estimate of the stability with respect to the number of collocation points.

T. Kitagawa | Takashi Kitagawa

[1] A. N. Tikhonov,et al. Solutions of ill-posed problems , 1977 .

[2] C. W. Groetsch,et al. The theory of Tikhonov regularization for Fredholm equations of the first kind , 1984 .

[3] S. Christiansen,et al. Condition number of matrices derived from two classes of integral equations , 1981 .

[4] A. Bogomolny. Fundamental Solutions Method for Elliptic Boundary Value Problems , 1985 .

[5] T. Kitagawa,et al. On the numerical stability of the method of fundamental solution applied to the Dirichlet problem , 1988 .

[6] T. Kitagawa. On the effectiveness of the method of regularization in numerical procedures for III-conditioned linear systems , 1988 .

[7] Gene H. Golub,et al. Matrix computations , 1983 .