Error estimation of floating-point summation and dot product

DOI10.1007/s10543-011-0342-4zbMath1243.65047OpenAlexW2001460356MaRDI QIDQ766234

Siegfried Michael Rump

Publication date: 23 March 2012

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-011-0342-4

zbMATH Keywords

error estimationerror boundsrounding errordirected roundingsdot productfloating-point summationunit in the first place(ufp)unit in the last place(ulp)

Mathematics Subject Classification ID

Roundoff error (65G50)

Related Items (12)

Generation of test matrices with specified eigenvalues using floating-point arithmetic ⋮ Simple floating-point filters for the two-dimensional orientation problem ⋮ Floating-point arithmetic on the test bench. How are verified numerical solutions calculated? ⋮ Error estimates for the summation of real numbers with application to floating-point summation ⋮ Fast floating-point filters for robust predicates ⋮ Floating-point arithmetic ⋮ On the maximum relative error when computing integer powers by iterated multiplications in floating-point arithmetic ⋮ Precision-aware deterministic and probabilistic error bounds for floating point summation ⋮ A Class of Fast and Accurate Summation Algorithms ⋮ Fast interval matrix multiplication ⋮ Numerical validation of compensated algorithms with stochastic arithmetic ⋮ Improvement of error-free splitting for accurate matrix multiplication

Uses Software

• mctoolbox

Cites Work

• Fast inclusion of interval matrix multiplication
• Ultimately Fast Accurate Summation
• Average-Case Stability of Gaussian Elimination
• Handbook of Floating-Point Arithmetic
• Accuracy and Stability of Numerical Algorithms
• Accurate Floating-Point Summation Part I: Faithful Rounding

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