计算具有多组重根的非亏损广义特征值问题特征矢导支配方程特解的混合法

A Mixed Method for Calculating Particular Solutions of Eigenvector Derivative Governing Equations in Nondefective Generalized Eigenproblems with Groups of Repeated Roots

提出在计算具有多组重根的非亏损广义特征值问题特征矢导支配方程特解时，先用直接法解第一组特解，然后用一族模态法求其余特解；文中的直接法以Gauss消去法为基础，在得到特解的同时，求得约束广义逆；导出各组重根的约束广义逆之间的换算式，从而减少总的计算量．

A mixed method for calculating particular solutions of eigenvector derivative equations in nondefective generalized eigenproblem with groups of repeated latent roots is presented, which finds the first set of particular solutions by direct method and other particular solutions by a family of modal methods. The direct method in this paper is based on Gaussian elimination, by which the constraint generalized inverse can be got as well the particular solutions. A formula for finding a constraint generalized inverse from another is derived, by which the total calculation can be notably reduced.