Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices

DOI10.1137/14098048XzbMath1325.65054arXiv1408.0042WikidataQ59695756 ScholiaQ59695756MaRDI QIDQ3196654

Eugene Vecharynski, Andrew V. Knyazev

Publication date: 30 October 2015

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.0042

zbMATH Keywords

linear systemseigenvalueeigenvectorHermitianabsolute value preconditioning

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Hermitian, skew-Hermitian, and related matrices (15B57) Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs (65M55) Preconditioners for iterative methods (65F08)

Related Items (6)

Preconditioned Eigensolvers for Large-Scale Nonlinear Hermitian Eigenproblems with Variational Characterizations. II. Interior Eigenvalues ⋮ A parallel eigensolver for photonic crystals discretized by edge finite elements ⋮ Iterative ILU Preconditioners for Linear Systems and Eigenproblems ⋮ Convergence proof of the harmonic Ritz pairs of iterative projection methods with restart strategies for symmetric eigenvalue problems ⋮ Generalized Preconditioned Locally Harmonic Residual Method for Non-Hermitian Eigenproblems ⋮ A generalization of Saad's bound on harmonic Ritz vectors of Hermitian matrices

Uses Software

• EIGIFP
• BLOPEX
• KSSOLV
• CIRR
• lobpcg.m

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fast iterative interior eigensolver for millions of atoms
• Computing interior eigenvalues of large matrices
• Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods
• Preconditioning eigensolvers -- an Oxymoron?
• Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems
• CIRR: a Rayleigh-Ritz method with contour integral for generalized eigenvalue problems
• Matrix Algorithms
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
• KSSOLV—a MATLAB toolbox for solving the Kohn-Sham equations
• Numerical Methods for Large Eigenvalue Problems
• A note on harmonic Ritz values and their reciprocals
• A Filtered Lanczos Procedure for Extreme and Interior Eigenvalue Problems
• A Rayleigh quotient minimization algorithm based on algebraic multigrid
• An algebraic multigrid wave–ray algorithm to solve eigenvalue problems for the helmholtz operator
• Algebraic multigrid methods for solving generalized eigenvalue problems
• Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) in Hypre and PETSc
• Solution of Sparse Indefinite Systems of Linear Equations
• Iterative Solution Methods
• A Multigrid Tutorial, Second Edition
• Templates for the Solution of Algebraic Eigenvalue Problems
• A new method for diagonalising large matrices
• An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
• Approximate solutions and eigenvalue bounds from Krylov subspaces
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• Harmonic projection methods for large non-symmetric eigenvalue problems
• Accuracy Properties of the Wave‐Ray Multigrid Algorithm for Helmholtz Equations
• Absolute Value Preconditioning for Symmetric Indefinite Linear Systems

This page was built for publication: Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices