On relative errors of floating-point operations: Optimal bounds and applications

DOI10.1090/mcom/3234zbMath1380.65082OpenAlexW2292537122MaRDI QIDQ4600709

Claude-Pierre Jeannerod, Siegfried Michael Rump

Publication date: 12 January 2018

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

Full work available at URL: https://hal.inria.fr/hal-00934443/file/JeannerodRump2016.pdf

zbMATH Keywords

floating-point arithmeticoptimal boundnumerical algorithmrounding error analyses

Mathematics Subject Classification ID

Roundoff error (65G50)

Related Items (11)

Formalization of Double-Word Arithmetic, and Comments on “Tight and Rigorous Error Bounds for Basic Building Blocks of Double-Word Arithmetic” ⋮ Floating-point arithmetic ⋮ Enabling floating-point arithmetic in the Coq proof assistant ⋮ On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic ⋮ Fast and accurate computation of the Euclidean norm of a vector ⋮ Precision-aware deterministic and probabilistic error bounds for floating point summation ⋮ Formally-verified round-off error analysis of Runge-Kutta methods ⋮ Primitive Floats in Coq ⋮ Efficient calculation of the joint distribution of order statistics ⋮ The relative accuracy of \(\mathtt{(x+y)*(x-y)}\) ⋮ A fast parallel high-precision summation algorithm based on AccSumK

Uses Software

• mctoolbox
• OEIS

Cites Work

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• Error analysis of floating-point computation
• A floating-point technique for extending the available precision
• Improved Error Bounds for Inner Products in Floating-Point Arithmetic
• Improved Backward Error Bounds for LU and Cholesky Factorizations
• Error bounds on complex floating-point multiplication with an FMA
• Error bounds on complex floating-point multiplication
• Implementing complex elementary functions using exception handling
• Accuracy and Stability of Numerical Algorithms
• Accurate Floating-Point Summation Part I: Faithful Rounding
• Midpoints and Exact Points of Some Algebraic Functions in Floating-Point Arithmetic
• Accurate Sum and Dot Product

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