A Thick-Restart Lanczos Algorithm with Polynomial Filtering for Hermitian Eigenvalue Problems
From MaRDI portal
Publication:2818245
DOI10.1137/15M1054493zbMath1348.65071arXiv1512.08135OpenAlexW2962736137MaRDI QIDQ2818245
Yuanzhe Xi, Chao Yang, Ruipeng Li, Eugene Vecharynski, Yousef Saad
Publication date: 7 September 2016
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1512.08135
deflationLanczos algorithmleast squares techniquepolynomial filteringspectrum slicingthick-restartinterior eigenvalue problems
Related Items
Beyond Automated Multilevel Substructuring: Domain Decomposition with Rational Filtering, A non-perturbative approach to computing seismic normal modes in rotating planets, Fast Computation of Spectral Densities for Generalized Eigenvalue Problems, Scalable implementation of polynomial filtering for density functional theory calculation in PARSEC, Hybrid eigensolvers for nuclear configuration interaction calculations, On flexible block Chebyshev-Davidson method for solving symmetric generalized eigenvalue problems, Solution of the \(k\)-th eigenvalue problem in large-scale electronic structure calculations, Explicit deflation in Golub-Kahan-Lanczos bidiagonalization methods, Computing the smallest singular triplets of a large matrix, On Chebyshev-Davidson method for symmetric generalized eigenvalue problems, TRPL+K: Thick-Restart Preconditioned Lanczos+K Method for Large Symmetric Eigenvalue Problems, Computational Materials Science and Engineering, The Lanczos Algorithm Under Few Iterations: Concentration and Location of the Output, Cucheb: a GPU implementation of the filtered Lanczos procedure, Solving large-scale interior eigenvalue problems to investigate the vibrational properties of the boson peak regime in amorphous materials, Hybrid Iterative Refined Method for Computing a Few Extreme Eigenpairs of a Symmetric Matrix, A Novel Algebraic Multigrid Approach Based on Adaptive Smoothing and Prolongation for Ill-Conditioned Systems, Evaluating non-analytic functions of matrices, Sharp error bounds for Ritz vectors and approximate singular vectors, The Eigenvalues Slicing Library (EVSL): Algorithms, Implementation, and Software, Numerical aspect of large-scale electronic state calculation for flexible device material, Hybrid Iterative Refined Method for Computing a Few Extreme Eigenpairs of a Symmetric Matrix, Polynomial Preconditioned Arnoldi with Stability Control, Computing interior eigenvalues of large sparse symmetric matrices
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- PRIMME
- A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix
- Strategies for spectrum slicing based on restarted Lanczos methods
- JADAMILU: a software code for computing selected eigenvalues of large sparse symmetric matrices
- The loss of orthogonality in the Gram-Schmidt orthogonalization process
- Self-consistent-field calculations using Chebyshev-filtered subspace iteration
- A projection method for generalized eigenvalue problems using numerical integration.
- Electronic structure calculations for plane-wave codes without diagonalization
- Rounding error analysis of the classical Gram-Schmidt orthogonalization process
- Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
- Approximating Spectral Densities of Large Matrices
- Anasazi software for the numerical solution of large-scale eigenvalue problems
- Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method
- Numerical Methods for Large Eigenvalue Problems
- A Filtered Lanczos Procedure for Extreme and Interior Eigenvalue Problems
- The Lanczos Algorithm With Partial Reorthogonalization
- SLEPc
- Practical Use of Polynomial Preconditionings for the Conjugate Gradient Method
- Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
- Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix
- Dynamic Thick Restarting of the Davidson, and the Implicitly Restarted Arnoldi Methods
- Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
- Numerical Methods for Electronic Structure Calculations of Materials
- Filtered Conjugate Residual‐type Algorithms with Applications
- Algorithm 827
- Computational Variants of the Lanczos Method for the Eigenproblem