Generalized conjugate gradient squared

DOI10.1016/0377-0427(95)00227-8zbMath0856.65021OpenAlexW1964233075MaRDI QIDQ1919946

Gerard L. G. Sleijpen, Diederik R. Fokkema, Henk A. van der Vorst

Publication date: 24 February 1997

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

Full work available at URL: https://doi.org/10.1016/0377-0427(95)00227-8

zbMATH Keywords

convergencenonlinear systemsnumerical examplesconjugate gradient squared methodKrylov subspacenonsymmetric linear systemsNewton's scheme

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Iterative numerical methods for linear systems (65F10)

Related Items

BiCGCR2: A new extension of conjugate residual method for solving non-Hermitian linear systems ⋮ Adomian's decomposition method applied to systems of nonlinear algebraic equations ⋮ Variations of Zhang's Lanczos-type product method ⋮ Reliable updated residuals in hybrid Bi-CG methods ⋮ A theoretical overview of Krylov subspace methods ⋮ An overview of approaches for the stable computation of hybrid BiCG methods ⋮ Hybrid Bi-CG methods with a Bi-CG formulation closer to the IDR approach ⋮ IDR: a new generation of Krylov subspace methods? ⋮ Cross-Interactive Residual Smoothing for Global and Block Lanczos-Type Solvers for Linear Systems with Multiple Right-Hand Sides ⋮ Accelerated Inexact Newton Schemes for Large Systems of Nonlinear Equations ⋮ A hybridized iterative algorithm of the BiCORSTAB and GPBiCOR methods for solving non-Hermitian linear systems ⋮ BiCR variants of the hybrid BiCG methods for solving linear systems with nonsymmetric matrices ⋮ Newton-preconditioned Krylov subspace solvers for system of nonlinear equations: A numerical experiment ⋮ Variants of residual smoothing with a small residual gap ⋮ Generalized global conjugate gradient squared algorithm ⋮ A fast numerical framework to compute acoustic scattering by poroelastic plates of arbitrary geometry ⋮ Unnamed Item ⋮ Iterative solution of linear systems in the 20th century

Uses Software

• Bi-CG
• BiCGstab
• CGS
• PILS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rational Krylov algorithms for nonsymmetric eigenvalue problems. II: Matrix pairs
• BiCGstab(\(l\)) and other hybrid Bi-CG methods
• BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
• Maintaining convergence properties of BiCGStab methods in finite precision arithmetic
• Reliable updated residuals in hybrid Bi-CG methods
• Hybrid Krylov Methods for Nonlinear Systems of Equations
• Continuation-Conjugate Gradient Methods for the Least Squares Solution of Nonlinear Boundary Value Problems
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Inexact Newton Methods
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• How Fast are Nonsymmetric Matrix Iterations?
• An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
• A class of first order factorization methods
• Variants of BICGSTAB for Matrices with Complex Spectrum
• Residual Smoothing Techniques for Iterative Methods
• A Quasi-Minimal Residual Variant of the Bi-CGSTAB Algorithm for Nonsymmetric Systems
• Semiconductor device modelling from the numerical point of view
• A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems