Parallelizable restarted iterative methods for nonsymmetric linear systems. part I: Theory

DOI10.1080/00207169208804107zbMath0759.65008OpenAlexW2127022449MaRDI QIDQ4021069

Graham F. Carey, Wayne D. Joubert

Publication date: 17 January 1993

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207169208804107

zbMATH Keywords

cachealgorithmsChebyshev polynomialsiterative methodfinite differenceKrylov spaceparallelHessenberg matrixconvection diffusion equationorthominnonsymmetric matrixNumerical testsconjugate gradient type methodGMRES/Chebyshev basis algorithm

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Iterative numerical methods for linear systems (65F10) Parallel numerical computation (65Y05) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (14)

Polynomial Preconditioned GMRES and GMRES-DR ⋮ A parallel implementation of the restarted GMRES iterative algorithm for nonsymmetric systems of linear equations ⋮ Randomized Sketching for Krylov Approximations of Large-Scale Matrix Functions ⋮ A restarted induced dimension reduction method to approximate eigenpairs of large unsymmetric matrices ⋮ On the generation of Krylov subspace bases ⋮ GMRES algorithms over 35 years ⋮ Tridiagonal Toeplitz matrices: properties and novel applications ⋮ Varying the \(s\) in your \(s\)-step GMRES ⋮ On IOM(q): The Incomplete Orthogonalization Method for Large Unsymmetric Linear Systems ⋮ Communication lower bounds and optimal algorithms for numerical linear algebra ⋮ The Stability of Block Variants of Classical Gram--Schmidt ⋮ On the cost of iterative computations ⋮ An adaptive \(s\)-step conjugate gradient algorithm with dynamic basis updating. ⋮ Accuracy of the $s$-Step Lanczos Method for the Symmetric Eigenproblem in Finite Precision

Cites Work

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• Variational Iterative Methods for Nonsymmetric Systems of Linear Equations
• A Taxonomy for Conjugate Gradient Methods
• Necessary and Sufficient Conditions for the Existence of a Conjugate Gradient Method
• Implementation of the GMRES Method Using Householder Transformations
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• A parallel element-by-element solution scheme
• Orthogonal Error Methods

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