An improved GBPi-CG algorithm suitable for distributed parallel computing

DOI10.1016/j.amc.2009.11.044zbMath1186.65041OpenAlexW2060561661MaRDI QIDQ961601

Tong-Xiang Gu, Ze-Yao Mo, Xian-Yu Zuo

Publication date: 31 March 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2009.11.044

zbMATH Keywords

numerical exampleKrylov subspaceglobal communicationdistributed parallel environmentsgeneralized product-type bi-conjugate gradient methodIGPBi-CG methodsparse unsymmetrical linear systems

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Iterative numerical methods for linear systems (65F10) Parallel numerical computation (65Y05) Complexity and performance of numerical algorithms (65Y20)

Related Items (3)

Minimizing synchronizations in sparse iterative solvers for distributed supercomputers ⋮ The non-symmetric \(s\)-step Lanczos algorithm: derivation of efficient recurrences and synchronization-reducing variants of BiCG and QMR ⋮ Alternating Anderson-Richardson method: an efficient alternative to preconditioned Krylov methods for large, sparse linear systems

Uses Software

• GpBiCg

Cites Work

• A performance model for Krylov subspace methods on mesh-based parallel computers
• An improved bi-conjugate residual algorithm suitable for distributed parallel computing
• An extension of the conjugate residual method to nonsymmetric linear systems
• QMR: A quasi-minimal residual method for non-Hermitian linear systems
• Reducing the effect of global communication in \(\text{GMRES} (m)\) and CG on parallel distributed memory computers
• A parallel version of QMRCGSTAB method for large linear systems in distributed parallel environments
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• On Deriving the Quasi-Minimal Residual Method
• GPBi-CG: Generalized Product-type Methods Based on Bi-CG for Solving Nonsymmetric Linear Systems
• Multiple search direction conjugate gradient method I: methods and their propositions
• Methods of conjugate gradients for solving linear systems
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