SINE TRANSFORM PRECONDITIONERS FOR SECOND-ORDER PARTIAL DIFFERENTIAL EQUATIONS

作     者：金小庆 

作者机构：Faculty of Science and Technology University of Macao Macao. 

出 版 物：《Numerical Mathematics A Journal of Chinese Universities(English Series)》 (高等学校计算数学学报(英文版))

年 卷 期：1993年第2卷第1期

页      面：116-123页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Sine Transform finite difference method second-order partial differential equation condition number preconditioned conjugate gradient method 

摘      要：In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale.