求解对称三对角矩阵特征值的一种新的分而治之算法  

A NEW DIVIDE-AND-CONQUER ALGORITHM FOR THE EIGENVALUE PROBLEM OF SYMMETRIC TRIDIAGONAL MATRICES

作　　者：罗晓广[1] 李晓梅[1] 

机构地区：[1]国防科技大学计算机系

出　　处：《数值计算与计算机应用》1997年第1期74-80,共7页Journal on Numerical Methods and Computer Applications

摘　　要：This paper presents a new divide-and-conquer algorithm for the eigenvalue problem ofsymmtric tridiagonal matrices. The new algorithm bases on bisection and secant iteration,which is different from Cuppen’s method and Laguerre iteration. The results of theoreticalanalysis and numerical testing show that the convergent rate of our algorithm is obviouslyfaster than that of Laguerre iteration presented in [1]. When the problem scale is quite.large, with the same requirement of accuracy, more than 40% of the computing time canbe reduced by using this new algorithm. In the end, we parallelize this new algorithm andget satisfactory testing results.This paper presents a new divide-and-conquer algorithm for the eigenvalue problem ofsymmtric tridiagonal matrices. The new algorithm bases on bisection and secant iteration,which is different from Cuppen's method and Laguerre iteration. The results of theoreticalanalysis and numerical testing show that the convergent rate of our algorithm is obviouslyfaster than that of Laguerre iteration presented in [1]. When the problem scale is quite.large, with the same requirement of accuracy, more than 40% of the computing time canbe reduced by using this new algorithm. In the end, we parallelize this new algorithm andget satisfactory testing results.

关 键 词：特征值 对称三对角矩阵 分而治之算法 矩阵 

分 类 号：O241.6[理学—计算数学]