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.
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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.
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Citations
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FEAST as a Subspace Iteration Eigensolver Accelerated by Approximate Spectral Projection
Ping Tak Peter Tang,Eric Polizzi +1 more
TL;DR: In this article, the authors present a detailed numerical analysis of the FEAST algorithm and show that it can be interpreted as an accelerated subspace iteration algorithm in conjunction with the Rayleigh-Ritz procedure.
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Highly Parallel Computation of Generalized Eigenvalue Problem in Vibration for Automatic Transmission of Vehicles Using the Sakurai–Sugiura Method and Supercomputers
Takanori Ide,Yuto Inoue,Yasunori Futamura,Tetsuya Sakurai +3 more
- 01 Jan 2017
TL;DR: This study presents a performance of a hierarchical parallel eigensolver using state-of-the-art supercomputers such as the K computer and COMA to solve the large-scale eigenvalue problem in automatic transmission of vehicles.
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A study on eigensolutions of 2D elastic problem by using BEM and FEM
Haifeng Gao,Toru Takahashi,Hiroshi Isakari +2 more
- 01 Nov 2013
TL;DR: In this article, Nagoya University (Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan, ttaka@nuem.nagoya-u.ac.jp)
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A FEAST variant incorporated with a power iteration.
Man-Chung Yeung,Long Lee +1 more
TL;DR: A variant of the FEAST matrix eigensolver for solving restricted real and symmetric eigenvalue problems that does not require that the search subspace dimension must be greater than or equal to the number of eigenvalues inside a search interval, and can deal with narrow search intervals more effectively.
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An efficient contour integral based eigensolver for 3D dispersive photonic crystal
TL;DR: An efficient contour integral (CI) based eigensolver is developed to overcome the difficulties of applying existing methods to solve eigenvalues in designated regions and illustrates the efficiency of this algorithm.
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References
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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.
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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.
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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.
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