The quadratic eigenvalue problem

被引：1004

作者：

Tisseur, F ^{[1
]}

Meerbergen, K

机构：

[1] Univ Manchester, Dept Math, Manchester M13 9PL, Lancs, England

[2] Free Field Technol, B-1348 Louvain, Belgium

来源：

SIAM REVIEW | 2001年 / 43卷 / 02期

关键词：

quadratic eigenvalue problem; eigenvalue; eigenvector; lambda-matrix; matrix polynomial; second-order differential equation; vibration; Millennium footbridge; overdamped system; gyroscopic system; linearization; backward error; pseudospectrum; condition number; Krylov methods; Arnoldi method; Lanczos method; Jacobi-Davidson method;

D O I：

10.1137/S0036144500381988

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse. real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software.

引用

页码：235 / 286

页数：52

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