The quadratic eigenvalue problem

被引：981
|
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
收藏
页码：235 / 286
页数：52
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