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
A FEAST SVDsolver based on Chebyshev--Jackson series for computing partial singular triplets of large matrices
08 Jan 2022
TL;DR: In this paper , the authors extended the FEAST eigensolver to the computation of the singular triplets of a large matrix with the singular values in a given interval, and proposed a robust alternative that constructs approximate spectral projectors by using the Chebyshev--Jackson polynomial series, which are symmetric positive semi-definite with the eigenvalues in $[0,1]$.
A method for finding zeros of polynomial equations using a contour integral based eigensolver
Tetsuya Sakurai,Junko Asakura,Hiroto Tadano,Tsutomu Ikegami,Kinji Kimura +4 more
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TL;DR: A numerical eigensolver using contour integral for a polynomial eigenvalue problem that is derived fromPolynomial equations is applied and the singular value decomposition for a matrix which appears in the eIGensolver is applied.
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A FEAST SVDsolver Based on Chebyshev–Jackson Series for Computing Partial Singular Triplets of Large Matrices
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Verified eigenvalue and eigenvector computations using complex moments and the Rayleigh–Ritz procedure for generalized Hermitian eigenvalue problems
TL;DR: In this paper , 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$\unicode{x2013}$Ritz procedure to project a given eigen value problem into a reduced Eigenvalue problem.
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A map of contour integral-based eigensolvers for solving generalized eigenvalue problems
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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.
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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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