关于带Rayleigh商位移的QL方法

On the QL Algorithm with Rayleigh Quotient Shift

本文讨论带Rayleigh商位移的QL方法的收敛性。给出了带Rayleigh商位移QL方法的收敛条件,并给出了带Rayleigh商位移QL方法不收敛的充分必要条件,证明了带Rayleigh商位移QL方法对任何不可约对称三对角矩阵总是有效的。

In this paper, the convergence and non-convergence of the QL algorithm with the Rayleigh quotient shift (called RQL algorithm) are discussed. The sufficient condition for the convergence of the RQL algorithm is given. The sufficient and necessary conditions for the non-convergence of the RQL algorithm are established. It is shown that the RQL algorithm is always efficient for any irreducible, symmetric, and tridiagonal matrices.