New methods for calculations of the lowest eigenvalues of the real symmetric generalized eigenvalue problem

DOI10.1006/jcph.2000.6520zbMath0964.65036OpenAlexW2086020387MaRDI QIDQ1578093

Alexander V. Mitin

Publication date: 26 June 2001

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcph.2000.6520

zbMATH Keywords

convergencecomparison of methodsnumerical examplesgeneralized eigenvalue problemNewton methodsmallest eigenvalueKrylov subspace methodJacobi-Davidson method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items

JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices, Orthogonal projection method for eigenpair derivatives of large symmetric matrices

Uses Software

• DVDSON

Cites Work

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• Modification of the Liu-Davidson method for obtaining one or simultaneously several eigensolutions of a large real-symmetric matrix
• Davidson's method and preconditioning for generalized eigenvalue problems
• Analysis of the symmetric Lanczos algorithm with reorthogonalization methods
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Computing eigenvalues of very large symmetric matrices. An implementation of a Lanczos algorithm with no reorthogonalization
• Improved algorithms for the lowest few eigenvalues and associated eigenvectors of large matrices
• The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
• A parallel Davidson-type algorithm for several eigenvalues
• Applications of the Lanczos method
• Towards a black box Lanczos program
• An implicit restarted Lanczos method for large symmetric eigenvalue problems
• A Davidson program for finding a few selected extreme eigenpairs of a large, sparse, real, symmetric matrix
• Projective block Lanczos algorithm for dense, Hermitian eigensystems
• Robust preconditioning of large, sparse, symmetric eigenvalue problems
• Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems
• An iterative method for finding characteristic vectors of a symmetric matrix
• Alternative correction equations in the Jacobi-Davidson method
• The Lanczos Algorithm With Partial Reorthogonalization
• Generalizations of Davidson’s Method for Computing Eigenvalues of Sparse Symmetric Matrices
• Davidson's algorithm with and without perturbation corrections
• The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
• Solving Sparse Symmetric Generalized Eigenvalue Problems without Factorization
• A Generalized Lanczos Scheme
• The Lanczos Algorithm with Selective Orthogonalization
• A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
• The Davidson Method
• Iterative Solution Methods
• Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods
• Preconditioning the Lanczos Algorithm for Sparse Symmetric Eigenvalue Problems
• A new method for diagonalising large matrices
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• Computational Variants of the Lanczos Method for the Eigenproblem
• The density matrix in may-electron quantum mechanics III. Generalized product functions for beryllium and four-electron ions
• Electronic wave functions II. A calculation for the ground state of the beryllium atom