Restarted generalized Krylov subspace methods for solving large-scale polynomial eigenvalue problems

被引：10
|
作者：
Bao, Liang [1 ]
Lin, Yiqin [2 ]
Wei, Yimin [3 ,4 ]
机构：
[1] E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China
[2] Hunan Univ Sci & Engn, Dept Math & Computat Sci, Yongzhou 425006, Peoples R China
[3] Fudan Univ, Sch Math Sci, Inst Math, Shanghai 200433, Peoples R China
[4] Fudan Univ, Minist Educ, Key Lab Math Nonlinear Sci, Beijing, Peoples R China
来源：
NUMERICAL ALGORITHMS | 2009年 / 50卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Polynomial eigenvalue problem; Generalized Krylov subspace; Generalized Arnoldi procedure; Projection technique; Refined technique; Restarting; MATRIX POLYNOMIALS; ARNOLDI METHOD; EIGENPROBLEMS; PSEUDOSPECTRA;
D O I：
10.1007/s11075-008-9214-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we introduce a generalized Krylov subspace G(m)(A;u) based on a square matrix sequence {A(j)} and a vector sequence {u(j)}. Next we present a generalized Arnoldi procedure for generating an orthonormal basis of G(m)(A;u). By applying the projection and the refined technique, we derive a restarted generalized Arnoldi method and a restarted refined generalized Arnoldi method for solving a large-scale polynomial eigenvalue problem (PEP). These two methods are applied to solve the PEP directly. Hence they preserve essential structures and properties of the PEP. Furthermore, restarting reduces the storage requirements. Some theoretical results are presented. Numerical tests report the effectiveness of these methods.
引用
收藏
页码：17 / 32
页数：16
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