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
On the non-Hermitian FEAST algorithms with oblique projection for eigenvalue problems
TL;DR: A new non-Hermitian scheme is presented for the FEAST algorithm, which also uses the oblique projection technique to extract the desired eigenpairs and the convergence properties studied are studied.
2
An Elementary Derivation of the Projection Method for Nonlinear Eigenvalue Problems Based on Complex Contour Integration
Yusaku Yamamoto
- 14 Sep 2015
TL;DR: In this article, an elementary derivation of the Sakurai-Sugiura (SS) projection method for the generalized eigenvalue problem has been presented, assuming that the wanted eigenvalues are all simple.
2
An Improved Contour-Integral Algorithm for Calculating Critical Eigenvalues of Power Systems Based on Accurate Number Counting
01 Jan 2023
TL;DR: In this paper , an improved contour-integral algorithm based on exact number counting inside the interesting region to calculate critical eigenvalues of large-scale power systems is proposed.
2
Efficient and Scalable Calculation of Complex Band Structure using Sakurai-Sugiura Method
TL;DR: The basic idea is to express the Kohn-Sham equation of the real-space grid scheme as a quadratic eigenvalue problem and compute only the solutions which are necessary to construct the CBS by Sakurai-Sugiura method.
1
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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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