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
Complex band structure calculations based on the overbridging boundary matching method without using Green's functions
TL;DR: In this paper, the authors formulated the Kohn-Sham equation for generalized Bloch wave functions as a generalized eigenvalue problem without using any Green's function matrix and used the Sakurai-Sugiura projection method to solve it.
Non-linear Least-Squares Optimization of Rational Filters for the Solution of Interior Hermitian Eigenvalue Problems
Jan Winkelmann,Edoardo Di Napoli +1 more
TL;DR: This work presents a framework for the optimization of rational filters based on a non-convex weighted Least-Squares scheme, and produces filter functions with specific properties that may be beneficial to the performance of the eigensolver that employs them.
On restarted and deflated block FOM and GMRES methods for sequences of shifted linear systems
TL;DR: Two new block projection methods based on respectively block FOM and block GMRES are introduced for solving sequences of shifted linear systems by expressing the original problem explicitly by a sequence of Sylvester matrix equations whose coefficient matrices are obtained from the shiftedlinear systems.
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Computing spectral properties of topological insulators without artificial truncation or supercell approximation
Peter Youngs
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TL;DR: In this article , the spectral properties of topological insulators have been investigated in the presence of material defects, edges, and disorder in the Haldane model, and spectral properties can be computed in two and three dimensions.
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Multi-Eigenvalue Demodulation Using Complex Moment-Based Eigensolver and Neural Network
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TL;DR: In this paper , the authors proposed a novel optical eigenvalue demodulation method that combines CME and an artificial neural network (ANN) based on employing an on-off encoded discrete eigen value modulation scheme.
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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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