Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods

DOI10.1016/0024-3795(80)90165-2zbMath0463.65025OpenAlexW2055251260MaRDI QIDQ1153647

Publication date: 1980

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(80)90165-2

zbMATH Keywords

conjugate-gradient acceleration nonsymmetrizable iterative methods

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items

New Optimized Robin--Robin Domain Decomposition Methods using Krylov Solvers for the Stokes--Darcy System, Properties of semi-conjugate gradient methods for solving unsymmetric positive definite linear systems, nlTGCR: A Class of Nonlinear Acceleration Procedures Based on Conjugate Residuals, The influence of the order of fill‐in on the convergence rate for ILU preconditioned iterative solvers, A priori pivoting in incomplete Gaussian preconditioning for iterative solution of mixed finite-element formulation of the Navier-Stokes equations, An efficient BE iterative-solver-based substructuring algorithm for 3D time-harmonic problems in elastodynamics., Recursive interpolation algorithm: A formalism for solving systems of linear equations. II: Iterative methods, An EM-based iterative method for solving large sparse linear systems, Unnamed Item, Unnamed Item, Variations of the GMRES iterative method, Variants of the groupwise update strategy for short-recurrence Krylov subspace methods, A generalized conjugate gradient, least square method, Minimal polynomial and reduced rank extrapolation methods are related, An iterative solution method for solving sparse nonsymmetric linear systems, A historical overview of iterative methods, An overview of NSPCG: A nonsymmetric preconditioned conjugate gradient package, Implementations of the GMRES method, A block preconditioned conjugate gradient-type iterative solver for linear systems in thermal reservoir simulation, Treatment of near-breakdown in the CGS algorithm, BiCGstab(\(l\)) and other hybrid Bi-CG methods, Conjugate residual methods for almost symmetric linear systems, An efficient implementation for SSOR and incomplete factorization preconditionings, A 3-D Poisson solver based on conjugate gradients compared to standard iterative methods and its performance on vector computers, Preconditioned conjugate residual methods for the solution of spectral equations, On the squared unsymmetric Lanczos method, Necessary and sufficient conditions for the simplification of generalized conjugate-gradient algorithms, Block and full matrix ILU preconditioners for parallel finite element solvers, A framework for generalized conjugate gradient methods -- with special emphasis on contributions by Rüdiger Weiß, A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations, Iterative methods for overflow queuing models. II, Adaptive version of simpler GMRES, On iterative solution of linear equations arising in BVPs of ODEs, Look-ahead in Bi-CGSTAB and other product methods for linear systems, Generalized conjugate directions, Extrapolation vs. projection methods for linear systems of equations, Preconditioned steepest descent-like methods for symmetric indefinite systems, Projection-minimization methods for nonsymmetric linear systems, Domain decomposition algorithms for spectral methods, Maintaining convergence properties of BiCGStab methods in finite precision arithmetic, A new taxonomy of conjugate gradient methods, The methods of Vorobyev and Lanczos, The prolonged adaptive multigrid method for finite element Navier-Stokes equations, A brief review of the ITPACK project, Conjugate gradient type methods and preconditioning, Preconditioned Locally Harmonic Residual Method for Computing Interior Eigenpairs of Certain Classes of Hermitian Matrices, An iterative method for symmetric solutions and optimal approximation solution of the system of matrix equations \(A_{1}XB_{1} = C_{1}, A_{2}XB_{2} = C_{2}\), Spectral distribution of preconditioned elliptic operators, An application of the discrete-time Toda lattice to the progressive algorithm by Lanczos and related problems, A local solution adapted Tri-Tree multigrid generator and iterative equation solver for mixed finite element formulation of the Navier-Stokes equations, Roundoff error analysis of algorithms based on Krylov subspace methods, Residual smoothing and peak/plateau behavior in Krylov subspace methods, Preconditioned cg‐like methods for solving non‐linear convection—diffusion equations, A preconditioned alternating inner‐outer iterative solution method for the mixed finite element formulation of the Navier‐Stokes equations, Hybrid MPE-iterative schemes for linear and nonlinear systems, Block jacobi preconditioning of the conjugate gradient method on a vector processor, Parallelizable restarted iterative methods for nonsymmetric linear systems. part I: Theory, Explicit approximate inverse preconditioning techniques, The use of conjugate gradients methods with a segregated finite volume procedure for solving transient, incompressible Navier–Stokes equations, Residual iterative method for solving absolute value equations, Generalized conjugate-gradient acceleration of nonsymmetrizable iterative methods, A survey of multilevel preconditioned iterative methods, A fast implementation for GMRES method, GMRES algorithms over 35 years, Efficient implementation of minimal polynomial and reduced rank extrapolation methods, Performance of hyperplane ordering on vector computers, Using successive approximations for improving the convergence of GMRES method, Projection methods for linear systems, Preconditioned gradient type methods applied to nonsymmetric linear systems, Breakdowns in the implementation of the Lánczos method for solving linear systems, Parallel implementation of BVM methods, The block grade of a block Krylov space, A cost comparison of boundary element and finite element methods for problems of time-harmonic acoustics, Accelerated Inexact Newton Schemes for Large Systems of Nonlinear Equations, Distributed minimal residual (DMR) method for acceleration of iterative algorithms, On IOM(q): The Incomplete Orthogonalization Method for Large Unsymmetric Linear Systems, Simulating vortex induced vibration of an impulsively started flexible filament by an implicit IB-LB coupling scheme, A fast parallel Poisson solver on irregular domains applied to beam dynamics simulations, Left conjugate gradient method for non‐Hermitian linear systems, Efficient a priori pivoting schemes for a sparse direct Gaussian equation solver for the mixed finite element formulation of the Navier-Stokes equations, Lanczos-type algorithms for solving systems of linear equations, A general projection algorithm for solving systems of linear equations, Comparison of Lanczos and CGS solvers for solving numerical heat transfer problems, Data structures to vectorize CG algorithms for general sparsity patterns, Adaptive polynomial preconditioning for Hermitian indefinite linear systems, Preconditioned minimal residual methods for Chebyshev spectral calculations, Chebyshev acceleration of the method of Cimmino, On IGMRES: An incomplete generalized minimal residual method for large unsymmetric linear systems, A simple ILU preconditioning coupled to orthomin method, On vector Hankel determinants, Iterative methods for linear systems of equations: A brief historical journey, A new implementation of EN method, Iterative techniques for rough surface scattering problems, On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems, Incomplete factorization methods for three-dimensional non-symmetric problems, Iterative solution of linear systems in the 20th century, The matrix and polynomial approaches to Lanczos-type algorithms, Numerical linear algebra algorithms and software, Hierarchical bases of finite-element spaces in the discretization of nonsymmetric elliptic boundary value problems, Nonlinear orthomin\((k)\) methods, Spectral methods for exterior elliptic problems, On the performance of certain direct and iterative methods on equations arising on a two-dimensional in situ combustion simulator, Modified Lanczos method for solving large sparse linear systems, A review of formal orthogonality in Lanczos-based methods, Using program package NSPCG to analyze the trunk reservation service protection method, A unified derivation for fast estimation algorithms by the conjugate direction method, Composite adaptive procedure for solving large sparse linear systems, Revisiting \((k,\ell)\)-step methods, A breakdown-free Lanczos type algorithm for solving linear systems, Numerical experiments of some Krylov subspace methods for black oil model

Cites Work