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
Integration based solvers for standard and generalized Hermitian eigenvalue problems
Lukas Krämer
- 22 Jan 2018
TL;DR: In this article, the authors discuss the numerically integration of Resolvente der Matrix (bzw. des======Matrix-Paares) and stellt sich heraus, dass das Problem, die Resolvatione zu integrieren, is equivalent zu einem gewissen approximation problem.
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Stability analysis of time-delay systems using a contour integral method
Xiao-Ping Chen,Hua Dai +1 more
TL;DR: A contour integral method for computing the rightmost characteristic roots of systems of linear time-delay differential equations (DDEs) and its effectiveness is illustrated by some numerical experiments.
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Eigenvalue analysis for 2D acoustic problem by BEM with block SS method
Haifeng Gao,Toshiro Matsumoto,Toru Takahashi,Takayuki Yamada +3 more
- 01 Dec 2011
TL;DR: In this paper, the authors used BEM and the block Sakurai-Sugiura Method (block SS method) to solve the eigenvalue problems governed by two-dimensional Helmholtz equation.
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ESSEX: Equipping Sparse Solvers For Exascale.
Christie L. Alappat,Andreas Alvermann,Achim Basermann,Holger Fehske,Yasunori Futamura,Martin Galgon,Georg Hager,Sarah Huber,Akira Imakura,Masatoshi Kawai,Moritz Kreutzer,Bruno Lang,Kengo Nakajima,Melven Röhrig-Zöllner,Tetsuya Sakurai,Faisal Shahzad,Jonas Thies,Gerhard Wellein +17 more
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TL;DR: The ESSEX project investigates computational issues arising at exascale for large-scale sparse eigenvalue problems and develops programming concepts and numerical methods for their solution.
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A FEAST Algorithm with oblique projection for generalized eigenvalue problems
TL;DR: This paper uses the oblique projection technique to extend FEAST to the non‐Hermitian problems and addresses some implementation issues such as how to choose a suitable starting matrix and design‐efficient stopping criteria.
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References
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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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