Computing eigenpairs in augmented Krylov subspace produced by Jacobi-Davidson correction equation

DOI10.1016/j.cam.2018.05.001zbMath1391.65088OpenAlexW2806644665MaRDI QIDQ1643856

Cun-Qiang Miao

Publication date: 20 June 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2018.05.001

zbMATH Keywords

Jacobi-Davidsonaugmented Krylov subspaceHermitian eigen-problem

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (11)

On global convergence of subspace projection methods for Hermitian eigenvalue problems ⋮ A Neural Network Approach to Sampling Based Learning Control for Quantum System with Uncertainty ⋮ A multilevel Newton's method for the Steklov eigenvalue problem ⋮ Accelerating the Arnoldi method via Chebyshev polynomials for computing PageRank ⋮ Image restoration by a mixed high-order total variation and \(l_1\) regularization model ⋮ Tikhonov regularized variable projection algorithms for separable nonlinear least squares problems ⋮ On relaxed filtered Krylov subspace method for non-symmetric eigenvalue problems ⋮ Behavior of the correction equations in the Jacobi-Davidson method ⋮ Computing eigenpairs of Hermitian matrices in augmented Krylov subspace produced by Rayleigh quotient iterations ⋮ Rayleigh quotient minimization method for symmetric eigenvalue problems ⋮ Filtered Krylov-like sequence method for symmetric eigenvalue problems

Uses Software

• EIGIFP
• JDQZ
• lobpcg.m

Cites Work

• Unnamed Item
• On local quadratic convergence of inexact simplified Jacobi-Davidson method
• Some modifications of Newton's method with higher-order convergence for solving nonlinear equations
• The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
• Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems
• On local quadratic convergence of inexact simplified Jacobi-Davidson method for interior eigenpairs of Hermitian eigenproblems
• Alternative correction equations in the Jacobi-Davidson method
• Toward the Optimal Preconditioned Eigensolver: Locally Optimal Block Preconditioned Conjugate Gradient Method
• Numerical Methods for Large Eigenvalue Problems
• Studies on Jacobi–Davidson, Rayleigh quotient iteration, inverse iteration generalized Davidson and Newton updates
• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• Analysis of Augmented Krylov Subspace Methods
• Preconditioning the Lanczos Algorithm for Sparse Symmetric Eigenvalue Problems
• An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• Combination of Jacobi–Davidson and conjugate gradients for the partial symmetric eigenproblem

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