Superlinear convergence estimates for a conjugate gradient method for the biharmonic equation

被引：4

作者：

Chan, RH ^{[1
]}

Delillo, TK

Horn, MA

机构：

[1] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong

[2] Wichita State Univ, Dept Math & Stat, Wichita, KS 67260 USA

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 1998年 / 19卷 / 01期

关键词：

biharmonic equation; numerical conformal mapping; Hankel matrices; conjugate gradient method;

D O I：

10.1137/S1064827596303570

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The method of Muskhelishvili for solving the biharmonic equation using conformal mapping is investigated. In [R. H. Chan, T. K. DeLillo, and M. A. Horn, SIAM J. Sci. Comput., 18 (1997), pp. 1571-1582] it was shown, using the Hankel structure, that the linear system in [N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, the Netherlands] is the discretization of the identity plus a compact operator, and therefore the conjugate gradient method will converge superlinearly. Estimates are given here of the superlinear convergence in the cases when the boundary curve is analytic or in a Holder class.

引用

页码：139 / 147

页数：9

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