General framework for deriving reproducible Krylov subspace algorithms: BiCGStab case

DOI10.1007/978-3-031-30442-2_2OpenAlexW4367356023MaRDI QIDQ6135460

Roman Iakymchuk, José I. Aliaga, Stef Graillat

Publication date: 25 August 2023

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

Full work available at URL: https://doi.org/10.1007/978-3-031-30442-2_2

zbMATH Keywords

accuracyreproducibilitypreconditioned BiCGStabfloating-point expansionlong accumulatorfused multiply-add

Mathematics Subject Classification ID

Parallel algorithms in computer science (68W10) Parallel numerical computation (65Y05)

Cites Work

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• The exact dot product as basic tool for long interval arithmetic
• Reproducibility strategies for parallel preconditioned conjugate gradient
• Parallel Reproducible Summation
• MPFR
• Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Accurate Sum and Dot Product

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