THE QUADRATIC ARNOLDI METHOD FOR THE SOLUTION OF THE QUADRATIC EIGENVALUE PROBLEM

被引：33
|
作者：
Meerbergen, Karl [1 ]
机构：
[1] Katholieke Univ Leuven, Dept Comp Sci, B-3001 Heverlee, Leuven, Belgium
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2008年 / 30卷 / 04期
关键词：
quadratic eigenvalue problem; Arnoldi method; SOAR method; Schur decomposition;
D O I：
10.1137/07069273X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The quadratic Arnoldi algorithm is a Krylov method for the solution of the quadratic eigenvalue problem, that exploits the structure of the Krylov vectors. This allows us to reduce the memory requirements by about a half. The method is an alternative to the second order Arnoldi (SOAR) method. In the SOAR method it is not clear how to perform an implicit restart. We discuss various choices of linearizations in L-1 and DL. We also explain how to compute a partial Schur form of the underlying linearization with respect to the structure of the Schur vectors. We also formulate some open problems.
引用
收藏
页码：1463 / 1482
页数：20
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