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
Eigenvalue computation in the 20th century
TL;DR: The intention of this contribution is to sketch the main developments of this century, especially as they relate to one another, and to give an impression of the state of the art at the turn of the authors' century.
482
A projection method for generalized eigenvalue problems using numerical integration
Tetsuya Sakurai,Hiroshi Sugiura +1 more
TL;DR: In this article, a method for finding certain eigenvalues of a generalized eigenvalue problem that lie in a given domain of the complex plane is proposed, which projects the matrix pencil onto a subspace associated with the eigen values that are located in the domain via numerical integration.
402
The spectral transformation Lánczos method for the numerical solution of large sparse generalized symmetric eigenvalue problems
Thomas Ericsson,Axel Ruhe +1 more
TL;DR: It is shown that for each shift several eigenvectors will converge after very few steps of the Lanczos algorithm, and the most effective combination of shifts and Lanczos runs is determined for different sizes and sparsity properties of the matrices.
•Journal Article
Solving Schrodinger's equation around a desired energy : Application to silicon quantum dots
Lin-Wang Wang,Alex Zunger +1 more
TL;DR: In this article, the authors present a linear-in-size method that enables the calculation of the eigensolutions of a Schrodinger equation in a desired energy window.
324