病态代数方程的精细积分解法

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...

Precise integration method for solving ill-conditioned algebraic equations

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.