The study of Jacobi and cyclic Jacobi matrix eigenvalue problems using Sturm–Liouville theory
نویسندگان
چکیده
منابع مشابه
The Jacobi-Davidson Method for Eigenvalue and Generalized Eigenvalue Problems
We consider variants of Davidson's method for the iterative computation of one or more eigenvalues and their corresponding eigenvectors of an n n matrix A. The original Davidson method 3], for real normal matrices A, may be viewed as an accelerated Gauss-Jacobi method, and the success of the method seems to depend quite heavily on diagonal dominance of A 3, 4, 17]. In the hope to enlarge the sc...
متن کاملJacobi-Davidson methods for cubic eigenvalue problems
Several Jacobi–Davidson type methods are proposed for computing interior eigenpairs of large-scale cubic eigenvalue problems. To successively compute the eigenpairs, a novel explicit non-equivalence de ation method with low-rank updates is developed and analysed. Various techniques such as locking, search direction transformation, restarting, and preconditioning are incorporated into the method...
متن کاملArnoldi and Jacobi - Davidson methods for generalized eigenvalue problems
In many physical situations, a few specific eigenvalues of a large sparse generalized eigenvalue problem Ax = λBx are needed. If exact linear solves with A − σB are available, implicitly restarted Arnoldi with purification is a common approach for problems where B is positive semidefinite. In this paper, a new approach based on implicitly restarted Arnoldi will be presented that avoids most of ...
متن کاملJacobi-Davidson methods for polynomial two-parameter eigenvalue problems
We propose Jacobi–Davidson type methods for polynomial two-parameter eigenvalue problems (PMEP). Such problems can be linearized as singular two-parameter eigenvalue problems, whose matrices are of dimension k(k + 1)n/2, where k is the degree of the polynomial and n is the size of the matrix coefficients in the PMEP. When k2n is relatively small, the problem can be solved numerically by computi...
متن کاملA Jacobi-Davidson Method for Solving Complex Symmetric Eigenvalue Problems
We discuss variants of the Jacobi–Davidson method for solving the generalized complex-symmetric eigenvalue problem. The Jacobi–Davidson algorithm can be considered as an accelerated inexact Rayleigh quotient iteration. We show that it is appropriate to replace the Euclidean inner product xy in C by the bilinear form x y. The Rayleigh quotient based on this bilinear form leads to an asymptotical...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2011
ISSN: 0024-3795
DOI: 10.1016/j.laa.2010.04.035