A fast parallel high-precision summation algorithm based on AccSumK

DOI10.1016/j.cam.2021.113827zbMath1482.65074OpenAlexW4200260987MaRDI QIDQ2074862

Hao Jiang, Xiao-Jun Lei, Jin Qi, Stef Graillat, Tong-Xiang Gu

Publication date: 11 February 2022

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

Full work available at URL: https://doi.org/10.1016/j.cam.2021.113827

zbMATH Keywords

parallel algorithmsfloating-point arithmeticaccurate summationhigher precision

Mathematics Subject Classification ID

Roundoff error (65G50) Numerical computation of matrix norms, conditioning, scaling (65F35) Parallel numerical computation (65Y05) Direct numerical methods for linear systems and matrix inversion (65F05) Software, source code, etc. for problems pertaining to linear algebra (15-04)

Related Items (3)

Parallel vectorized implementations of compensated summation algorithms ⋮ PAccSumK ⋮ AccSumK

Uses Software

• Matlab
• MPFR
• mctoolbox
• ReproBLAS

Cites Work

• Unnamed Item
• Inversion of extremely ill-conditioned matrices in floating-point
• Fast and accurate floating point summation with application to computational geometry
• Error estimates for the summation of real numbers with application to floating-point summation
• A floating-point technique for extending the available precision
• MPFR
• Accurate Floating-Point Summation Part II: Sign, K-Fold Faithful and Rounding to Nearest
• On relative errors of floating-point operations: Optimal bounds and applications
• Sharp estimates for perturbation errors in summations
• Accuracy and Stability of Numerical Algorithms
• Accurate Floating-Point Summation Part I: Faithful Rounding
• Accurate Sum and Dot Product

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