解对称带状矩阵特征值问题的二分法及其改进  

A BISECTION METHOD AND ITS MODIFICATION FOR SOLVING THE EIGENVALUE PROBLEM OF SYMMETRIC BAND MATRICES

作　　者：罗晓广[1] 李晓梅[1] 陈健华[2] 

机构地区：[1]国防科技大学计算机系 [2]国防科技大学应用物理系

出　　处：《计算物理》1997年第4期450-452,共3页Chinese Journal of Computational Physics

基　　金：国防预研课题

摘　　要：提出了解对称带状矩阵特征值问题的一种二分法。当仅需计算指定的部分特征值及其特征向量时，该方法尤其适合。进一步，我们还对二分法作改进。改进策略是：先用二分法计算若干步，得到特征值的近似值；然后从该近似值出发进行Ｒａｙｌｅｉｇｈ商迭代，直至其达到要求的精度为止。A bisection method is presented for solving the eigenvalue problem of symmetric band matrices.This method is especially suitable for the case where only a few eigenpairs are needed. Further more,a modified strategy is also presented.The main idea is that firstly using the bisection for some steps to obtain an approximate eigenvalue,then Rayleigh Quotient Iteration is applied to extract the eigenvalue to a predifined accuracy.

关 键 词：对称带状矩阵 矩阵特征值 二分法 瑞利商迭代 

分 类 号：O151.21[理学—数学]