上海大学学报（英文版）
上海大學學報（英文版）
상해대학학보（영문판）
JOURNAL OF SHANGHAI UNIVERSITY (ENGLISH EDITION)
2004年
4期
369-377
,共9页
matrix eigenvalue problem%symmetric tridiagonal matrix%QL(QR) algorithm%shift%error bound
QL(QR) method is an efficient method to find eigenvalues of a matrix. Especially we use QL(QR) method to find eigenvalues of a symmetric tridiagonal matrix. In this case it only costs O(n2) flops, to find all eigenvalues. So it is one of the most efficient method for symmetric tridiagonal matrices. Many experts have researched it. Even the method is mature, it still has many problems need to be researched. We put forward five problems here. They are: (1) Convergence and convergence rate; (2) The convergence of diagonal elements; (3) Shift designed to produce the eigenvalues in monotone order; (4) QL algorithm with multi-shift; (5) Error bound. We intoduce our works on these problems, some of them were published and some are new.
