Abstract: 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 a...