求解病态线性方程组的自动控制步长法

Automatic Step-size Control Algorithm for Solving Ill-conditioned Linear Equations

在Wilkinson迭代法的基础上,采用嵌入式的欧拉公式和二阶R-K方法,构造了求解病态线性方程组的迭代格式,讨论了其步长的确定,对迭代格式从hn是一个常量和hn是一个变量两个方面,证明了其收敛性,并验证了算法的有效性。

The iterative format to solve the ill-conditioned linear equations is constructed based on the Wilkinson＇ s iterative method with embedded Euler method and second-order R-K method, and the determination of step is dis- cussed. The convergence of iterative format is proved from two aspects with hn as an constant and ha as a variable, and the effectiveness of the proposed algorithm is verified.