Preconditioned Eigensolvers for Large-Scale Nonlinear Hermitian Eigenproblems with Variational Characterizations. II. Interior Eigenvalues

DOI10.1137/15M1016096zbMath1329.65108arXiv1504.02811OpenAlexW793949337MaRDI QIDQ3457835

Fei Xue, Eugene Vecharynski, Daniel B. Szyld

Publication date: 18 December 2015

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

Full work available at URL: https://arxiv.org/abs/1504.02811

zbMATH Keywords

convergencevariational principleconjugate gradient methodnumerical experimentinterior eigenvaluespreconditioned eigensolverRayleigh-Ritz projectionrefined projectioneigenpair extractionnonlinear Hermitian eigenproblem

Mathematics Subject Classification ID

Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17) Preconditioners for iterative methods (65F08)

Related Items (6)

Convergence theory for preconditioned eigenvalue solvers in a nutshell ⋮ Preconditioned steepest descent-like methods for symmetric indefinite systems ⋮ A Block Preconditioned Harmonic Projection Method for Large-Scale Nonlinear Eigenvalue Problems ⋮ On restarting the tensor infinite Arnoldi method ⋮ Preconditioned eigensolvers for large-scale nonlinear Hermitian eigenproblems with variational characterizations. I. Extreme eigenvalues ⋮ A survey on variational characterizations for nonlinear eigenvalue problems

Uses Software

• EIGIFP
• PARDISO
• QMRPACK
• NLEVP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hermitian matrix polynomials with real eigenvalues of definite type. I: Classification
• A linear eigenvalue algorithm for the nonlinear eigenvalue problem
• Restarting iterative projection methods for Hermitian nonlinear eigenvalue problems with minmax property
• Perturbation, extraction and refinement of invariant pairs for matrix polynomials
• Analyzing the convergence factor of residual inverse iteration
• Computing interior eigenvalues of large matrices
• A block Newton method for nonlinear eigenvalue problems
• Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems
• An Arnoldi method for nonlinear eigenvalue problems
• Software for simplified Lanczos and QMR algorithms
• Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems
• On Sylvester's law of inertia for nonlinear eigenvalue problems
• Rayleigh quotient iteration and simplified Jacobi-Davidson method with preconditioned iterative solves
• Iterative projection methods for computing relevant energy states of a quantum dot
• Variationsprinzipien bei nichtlinearen Eigenwertaufgaben
• Matrix Algorithms
• Robust Successive Computation of Eigenpairs for Nonlinear Eigenvalue Problems
• Computing a Partial Schur Factorization of Nonlinear Eigenvalue Problems Using the Infinite Arnoldi Method
• THE HYPERBOLIC QUADRATIC EIGENVALUE PROBLEM
• A minmax principle for nonlinear eigenproblems depending continuously on the eigenparameter
• NLEVP
• Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices
• Controlling Inner Iterations in the Jacobi–Davidson Method
• Residual Inverse Iteration for the Nonlinear Eigenvalue Problem
• A minimax principle for nonlinear eigenvalue problems with applications to nonoverdamped systems
• Solution of Sparse Indefinite Systems of Linear Equations
• Jacobi--Davidson Style QR and QZ Algorithms for the Reduction of Matrix Pencils
• Convergence Estimates for the Generalized Davidson Method for Symmetric Eigenvalue Problems II: The Subspace Acceleration
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• Absolute Value Preconditioning for Symmetric Indefinite Linear Systems
• On Large-Scale Diagonalization Techniques for the Anderson Model of Localization
• Algorithm 845
• A comparison of eigensolvers for large-scale 3D modal analysis using AMG-preconditioned iterative methods
• Weighted Matchings for Preconditioning Symmetric Indefinite Linear Systems
• Several properties of invariant pairs of nonlinear algebraic eigenvalue problems
• Preconditioned eigensolvers for large-scale nonlinear Hermitian eigenproblems with variational characterizations. I. Extreme eigenvalues

This page was built for publication: Preconditioned Eigensolvers for Large-Scale Nonlinear Hermitian Eigenproblems with Variational Characterizations. II. Interior Eigenvalues