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.
read more
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.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
A numerical method for nonlinear eigenvalue problems using contour integrals
TL;DR: A contour integral method is proposed to solve nonlinear eigenvalue problems numerically by reducing the original problem to a linear eigen value problem that has identical eigenvalues in the domain.
213
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.
162
Zolotarev quadrature rules and load balancing for the FEAST eigensolver
TL;DR: This work proposes improved rational approximants leading to FEAST variants with faster convergence, in particular, when using rational approximation based on the work of Zolotarev, and improves both convergence robustness and load balancing when FEAST runs on multiple search intervals in parallel.
118
Contour integral eigensolver for non-hermitian systems: a rayleigh-ritz-type approach
Tsutomu Ikegami,Tetsuya Sakurai +1 more
TL;DR: In this paper, the Rayleigh-Ritz-type approach of the contour integral eigensolver is extended to general applicability to non-Hermitian systems, which can extract only the eigenvalues in a given domain.
Feast Eigensolver for Non-Hermitian Problems
TL;DR: A detailed new upgrade of the FEAST eigensolver targeting non-Hermitian eigenvalue problems is presented and thoroughly discussed, aiming at broadening the class of eigenproblems that can be addressed within the framework of theFEAST algorithm.
References
Solving Schrödinger’s equation around a desired energy: Application to silicon quantum dots
Lin-Wang Wang,Alex Zunger +1 more
TL;DR: In this paper, the authors present a linear-in-size method that enables calculation of the eigensolutions of a Schrodinger equation in a desired energy window. And they illustrate this method by studying the near-gap electronic structure of Si quantum dots with size up to Si1315H460(≊37 A in diameter) using a plane wave pseudopotential representation.
Bound state eigenfunctions from wave packets: Time→energy resolution
TL;DR: In this paper, a method to obtain bound-state eigenfunctions in any arbitrary range of energies, by a Fourier resolution (from time to energy) of a real-time wave packet, is presented.
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
TL;DR: In this article, a new method for the iterative computation of a few extremal eigenvalues of a symmetric matrix and their associated eigenvectors is proposed, based on an old and almost unknown method of Jacobi.
A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices
TL;DR: A block version of Arnoldi's method for computing a few eigenvalues with largest or smallest real parts is described and a procedure is developed to identify the optimal ellipse which encloses the spectrum.
•Book
Numerical Methods for Large Eigenvalue Problems
Yousef Saad
- 22 Jun 1992
TL;DR: This chapter discusses matrix theory and linear algebra techniques used in spectral approximation, including Krylov subspace methods, and some of the origins of matrix eigenvalue problems.