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求解广义特征值问题的多重Ritz向量法

THE MULTI-RITZ-VECTOR METHOD IN GENERALIZED EIGENVALUE PROBLEMS

  • 摘要: 借鉴子空间迭代法,将求解广义特征值问题的单个初向量的Ritz向量法(下称为单R法)推广为多重Ritz向量法吓称为多R法);从而解决了单R法在处理重频结构时的漏频问题;且分析指出,奇异的矩阵M将导致一个数值不稳定的Gram-SchmidtM-正交化过程,从而使Ritz向量法导致错误振型.为此提出了解决方案.单R法经上述修正,兼备了高效与可靠两个特点.目前该法已在特殊多高层分析程序ETS5中实现,取得了良好效果.

     

    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...

     

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