Nonlinear eigenproblems

被引：21

作者：

Guillaume, P ^{[1
]}

机构：

[1] Univ Toulouse 3, INSA, CNRS, UMR 5640, F-31077 Toulouse, France

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1999年 / 20卷 / 03期

关键词：

nonlinear eigenproblem; polynomial eigenproblem; quadratic eigenproblem; generalized eigenproblem; Galerkin approximation; higher order derivatives;

D O I：

10.1137/S0895479897324172

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let A(lambda) be a holomorphic matrix-valued function defined on a domain Omega subset of C. The nonlinear eigenproblem of finding generalized eigenpairs lambda, upsilon such that A(lambda)upsilon = 0 is considered. The method which is exposed for solving this problem is based on the derivatives of the function x(lambda) = A(lambda)(-1) b, where b is a given vector. Theoretical convergence results are established, and an algorithm is proposed for computing a few eigenvalues close to a given complex number together with some corresponding eigenvectors.

引用

页码：575 / 595

页数：21

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