Verified numerical computations for large-scale linear systems.

DOI10.21136/AM.2021.0318-19OpenAlexW3122902324MaRDI QIDQ2662465

Takahiro Katagiri, Takeshi Terao, Katsuhisa Ozaki, Takeshi Ogita

Publication date: 13 April 2021

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.21136/am.2021.0318-19

zbMATH Keywords

floating-point arithmetichigh-performance computinglarge-scale linear systemverified numerical computation

Mathematics Subject Classification ID

Roundoff error (65G50) Parallel numerical computation (65Y05) Algorithms with automatic result verification (65G20)

Uses Software

• ScaLAPACK
• mctoolbox
• XBLAS
• MPACK
• PBLAS

Cites Work

• Unnamed Item
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• Improved Error Bounds for Inner Products in Floating-Point Arithmetic
• An efficient approach to solve very large dense linear systems with verified computing on clusters
• Iterative Refinement Implies Numerical Stability for Gaussian Elimination
• ScaLAPACK Users' Guide
• Accuracy and Stability of Numerical Algorithms
• A New Approach to Probabilistic Rounding Error Analysis
• Accurate Sum and Dot Product

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