QR分解与非线性特征值问题  

QR DECOMPOSITION AND NONLINEAR EIGENVALUE PROBLEMS

作　　者：李仁仓 

机构地区：[1]中国科学院计算中心

出　　处：《计算数学》1989年第4期374-385,共12页Mathematica Numerica Sinica

摘　　要：考察m×n矩阵A(λ),其中元素a_(ij)(λ)均为复(实)变量λ的解析(至少有一阶导数)函数.称此类矩阵为泛函λ-矩阵。特别,当a_(ij)(λ)是λ的多项式时,A(λ)就是熟知的λ-矩阵.给定A(λ)∈C^(n×n)(m=n),有时需确定其非线性特征值及其相应的特征向量。For a given differentiable functional λ-matrix A(λ) of order n, some differentiabilitytheorems for elements arising in its QR decompositions are proved, and several explicit expressi-ons for some derivatives are given. Based on these results, an algorithm for solving nonlineareigenvalue problems is proposed. By the way, it is pointed out that a counterexample given in[3] contains a fatal error. Also, extensions of these results to cases where A(λ) is not squareor λ is not a single variable are made. Sevaral numerical tests are presented.

关 键 词：QR分解 非线性 特征值问题 

分 类 号：O241.7[理学—计算数学]