Approximate solutions and eigenvalue bounds from Krylov subspaces
From MaRDI portal
Publication:4850230
DOI10.1002/nla.1680020205zbMath0831.65036OpenAlexW2170486042MaRDI QIDQ4850230
Christopher C. Paige, Beresford N. Parlett, Henk A. van der Vorst
Publication date: 9 October 1995
Published in: Numerical Linear Algebra with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/nla.1680020205
convergenceconjugate gradient methodKrylov subspace methodminimum residual methodeigenvalue boundsLanczos processlarge sparse symmetric system
Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10)
Related Items
Numerical methods for the QCDd overlap operator. I: Sign-function and error bounds, A harmonic restarted Arnoldi algorithm for calculating eigenvalues and determining multiplicity, A Preconditioned Hybrid SVD Method for Accurately Computing Singular Triplets of Large Matrices, Polynomial Preconditioned GMRES and GMRES-DR, A framework of the harmonic Arnoldi method for evaluating \(\varphi\)-functions with applications to exponential integrators, A modified harmonic block Arnoldi algorithm with adaptive shifts for large interior eigen\-problems, An invert-free Arnoldi method for computing interior eigenpairs of large matrices, Krylov methods and determinants for detecting bifurcations in one parameter dependent partial differential equations, Reliable updated residuals in hybrid Bi-CG methods, Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices, A note on the convergence behavior of GMRES, A hybrid iterative method for symmetric positive definite linear systems, New matrix function approximations and quadrature rules based on the Arnoldi process, On regularizing effects of MINRES and MR-II for large scale symmetric discrete ill-posed problems, Restarted block Lanczos bidiagonalization methods, A Block Preconditioned Harmonic Projection Method for Large-Scale Nonlinear Eigenvalue Problems, Large scale finite element computations with GMRES-like methods on a Cray Y-MP, Harmonic projection methods for large non-symmetric eigenvalue problems, An augmented LSQR method, Convergence proof of the harmonic Ritz pairs of iterative projection methods with restart strategies for symmetric eigenvalue problems, An adaptive Richardson iteration method for indefinite linear systems, Ritz and pseudo-Ritz values using matrix polynomials, Iterative methods for the computation of a few eigenvalues of a large symmetric matrix, Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems, Unnamed Item, Hessenberg matrices in krylov subspaces and the computation of the spectrum, Krylov subspace recycling for evolving structures, Abstract perturbed Krylov methods, The Convergence of Harmonic Ritz Vectors and Harmonic Ritz Values, Revisited, High-performance implementation of Chebyshev filter diagonalization for interior eigenvalue computations, The Radau--Lanczos Method for Matrix Functions, A multigrid accelerated eigensolver for the Hermitian Wilson-Dirac operator in lattice QCD, Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems, A new shifted block GMRES method with inexact breakdowns for solving multi-shifted and multiple right-hand sides linear systems, Limited memory preconditioners for symmetric indefinite problems with application to structural mechanics, Harmonic multi-symplectic Lanczos algorithm for quaternion singular triplets, Low-Memory Krylov Subspace Methods for Optimal Rational Matrix Function Approximation, Augmented and deflated CMRH method for solving nonsymmetric linear systems, The Coefficients of the FOM and GMRES Residual Polynomials, A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity, Deflated and restarted Krylov subspace methods for Sylvester tensor equations, A refined Arnoldi type method for large scale eigenvalue problems, Block Krylov Subspace Methods for Functions of Matrices II: Modified Block FOM, Solving the Trust-Region Subproblem By a Generalized Eigenvalue Problem, A flexible and adaptive simpler GMRES with deflated restarting for shifted linear systems, Fast iterative interior eigensolver for millions of atoms, On convergence of the inexact Rayleigh quotient iteration with MINRES, Parallelization of the Rational Arnoldi Algorithm, A harmonic framework for stepsize selection in gradient methods, Recycling Krylov subspaces for efficient large-scale electrical impedance tomography, On convergence of the inexact Rayleigh quotient iteration with the Lanczos method used for solving linear systems, On the initial estimate of interface forces in FETI methods., The behavior of symmetric Krylov subspace methods for solving \(Mx=(M-\gamma I)v\)., On the block GMRES method with deflated restarting, Thick restarting the weighted harmonic Arnoldi algorithm for large interior eigenproblems, State-of-the-art eigensolvers for electronic structure calculations of large scale nano-systems, A deflated conjugate gradient method for multiple right hand sides and multiple shifts, On a new variant of Arnoldi method for approximation of eigenpairs, New methods for computing the Drazin-inverse solution of singular linear systems, Irr: An algorithm for computing the smallest singular value of large scale matrices, A dynamically deflated GMRES adjoint solver for aerodynamic shape optimization, DGMRES and index numerical range of matrices, Optimal expansion of subspaces for eigenvector approximations, Deflated GMRES for systems with multiple shifts and multiple right-hand sides, Eigenvalue inclusion regions from inverses of shifted matrices, Accelerated Inexact Newton Schemes for Large Systems of Nonlinear Equations, A flexible and adaptive simpler block GMRES with deflated restarting for linear systems with multiple right-hand sides, Short-recurrence Krylov subspace methods for the overlap Dirac operator at nonzero chemical potential, The convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors, Restarted block-GMRES with deflation of eigenvalues, A limited memory steepest descent method, Fast eigenvalue calculations in a massively parallel plasma turbulence code, Time-evolution methods for matrix-product states, Two-Grid and Multiple-Grid Arnoldi for Eigenvalues, Closed-form control oriented model of highly flexible manipulators, A Parallel Implementation of the Jacobi-Davidson Eigensolver for Unsymmetric Matrices, Restarted GMRES augmented with harmonic Ritz vectors for shifted linear systems, A GMRES Convergence Analysis for Localized Invariant Subspace Ill-Conditioning, Computing smallest singular triplets with implicitly restarted Lanczos bidiagonalization, A parallel implementation of Davidson methods for large-scale eigenvalue problems in SLEPc, Convergence properties of block GMRES and matrix polynomials, Harmonic and refined extraction methods for the singular value problem, with applications in least squares problems, Improved seed methods for symmetric positive definite linear equations with multiple right‐hand sides, A hybrid iterative method for symmetric indefinite linear systems, Composite orthogonal projection methods for large matrix eigenproblems, Using implicitly filtered RKS for generalised eigenvalue problems, Restrictions on implicit filtering techniques for orthogonal projection methods, Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm, Polynomial Preconditioned Arnoldi with Stability Control, Eigenvalue computation in the 20th century, Analysis of acceleration strategies for restarted minimal residual methods, On the use of harmonic Ritz pairs in approximating internal eigenpairs, Analysis of the convergence of the minimal and the orthogonal residual methods, The refined harmonic Arnoldi method and an implicitly restarted refined algorithm for computing interior eigenpairs of large matrices, A refined harmonic Rayleigh-Ritz procedure and an explicitly restarted refined harmonic Arnoldi algorithm
Cites Work