THE MULTI-RITZ-VECTOR METHOD IN GENERALIZED EIGENVALUE PROBLEMS
求解广义特征值问题的多重Ritz向量法

With reference to the subspace iteration method, the normal Ritz-Vector methodis extended to an improved one i.e. the Multi-Ritz-Vector method in this paper by which theproblem of eigen-value losing for the systems with multi-fold eigen--value in the normal Ritz--Vectormethod can be solved and no eigen-vectors corresponding to multi-fold eigen--value will be lost.Then, it has been pointed out that a singular or ill-conditioned matrix M would lead to anunstable M-orthogonalization procedure of Gram-Schmidt and then yield incorrect eigen-vectorsif the normal Ritz--Vector method was directly used to a system with singular mass matrix. In theMulti-Ritz-Vector method, am elaborate algorithm is proposed in order to improve the stability ofthe computational procedure of the normal Ritz-Vector method. By incorporation of the abovetwo modifications, an improved method i.e. the Multi-Ritz-Vector method which is much moreefficient and reliable than the normal one is obtained.