病态代数方程的精细积分解法  

Precise integration method for solving ill-conditioned algebraic equations

作　　者：富明慧[1] 张文志[1] 

机构地区：[1]中山大学应用力学与工程系,广州510275

出　　处：《计算力学学报》2011年第4期530-534,共5页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(10672194);中俄NSFC-RFBR协议项目(10811120012)资助项目

摘　　要：基于精细积分思想,提出了一种有效的病态代数方程组求解方法。类似于稳态热传导方程可视为瞬态热传导方程的极限形式,将具有正定对称实系数矩阵的病态代数方程组归结为一个常微分方程组初值问题的极限形式,并在此基础上建立了病态代数方程组的精细积分解法。该方法不仅精度高,而且能以指数速度收敛,具有较高的效率。本文还讨论了病态代数方程组的系数矩阵非正定时的处理方法。算例证明了本文方法的有效性。An efficient method based on the idea of the precise integration method for solving ill-conditioned linear algebraic equations is presented.Similar to that the steady-state heat conduction equation can be regarded as the limit form of the transient heat conduction equation,the ill-conditioned algebraic equations with positive definite real coefficient matrix can be taken as a limit form of first-order ordinary differential equations with initial value problem.And on this basis,a precise integration method for solving ill-conditioned algebraic equations is established.The method has not only high precision but also high efficiency due to exponential rate of convergence.Additionally,the treatment of ill-conditioned algebraic equations with non-positive definite coefficient matrix is also discussed.Numerical examples show clearly the validity of the presented method.

关 键 词：病态代数方程组 病态矩阵 精细积分法 迭代算法 指数矩阵运算 

分 类 号：O242[理学—计算数学]