A filter diagonalization for generalized eigenvalue problems based on the Sakurai-Sugiura projection method
TL;DR: The Sakurai-Sugiura projection method, which solves generalized eigenvalue problems to find certain eigenvalues in a given domain, was reformulated by using the resolvent theory.
read more
About: This article is published in Journal of Computational and Applied Mathematics. The article was published on 01 Feb 2010. and is currently open access. The article focuses on the topics: Projection method & Eigenvalues and eigenvectors.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Posted Content
Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh-Ritz procedure for generalized Hermitian eigenvalue problems.
TL;DR: In this article, the authors proposed a verified computation method for eigenvalues in a region and the corresponding eigenvectors of generalized Hermitian eigenvalue problems, which uses complex moments to extract the eigencomponents of interest from a random matrix and uses the Rayleigh-Ritz procedure to project a given eigen value problem into a reduced Eigenvalue problem.
1
Filters consist of a few resolvents to solve real symmetric definite generalized eigenproblems
TL;DR: In present study, the filter is a polynomial of the real-part of a linear combination of a few resolvents, and thePolynomial is restricted to a Chebyshev Polynomial to make the design of the filter simple.
1
•Posted Content
Complex moment-based method with nonlinear transformation for computing large and sparse interior singular triplets.
Akira Imakura,Tetsuya Sakurai +1 more
TL;DR: In this paper, a novel complex moment-based method with a nonlinear transformation was proposed to compute interior singular triplets corresponding to the singular values in some interval, which is based on the concept of the complex moment based parallel eigensolvers.
1
•Posted Content
Projection method for partial eigenproblems of linear matrix pencils.
TL;DR: A projection method for square matrices to the singular non-square case is extended, and the proposed method does not fail for the existence of many pairs of extremely close eigenvalues and breaks the previous barrier of problem size.
1
Improvement of the accuracy of the approximate solution of the Block BiCR method
TL;DR: This paper proposes a modified Block BiCR method in order to improve the accuracy of the approximate solutions and shows a smooth convergence behavior compared with the Block BiCG method.
References
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
Youcef Saad,Martin H. Schultz +1 more
TL;DR: An iterative method for solving linear systems, which has the property of minimizing at every step the norm of the residual vector over a Krylov subspace.
The principle of minimized iterations in the solution of the matrix eigenvalue problem
TL;DR: In this paper, an interpretation of Dr. Cornelius Lanczos' iteration method, which he has named ''minimized iterations'' is discussed, expounding the method as applied to the solution of the characteristic matrix equations both in homogeneous and nonhomogeneous form.
•Book
Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide
James Demmel,Jack Dongarra,Axel Ruhe,Henk A. van der Vorst,Zhaojun Bai +4 more
- 01 Jan 1987
TL;DR: This book discusses iterative projection methods for solving Eigenproblems, and some of the techniques used to solve these problems came from the literature on Hermitian Eigenvalue.
1.6K
A Jacobi--Davidson Iteration Method for Linear Eigenvalue Problems
TL;DR: A new method for the iterative computation of a few of the extremal eigenvalues of a symmetric matrix and their associated eigenvectors is proposed that has improved convergence properties and that may be used for general matrices.
559