The functions erf and erfc computed with arbitrary precision and explicit error bounds

DOI10.1016/j.ic.2011.09.001zbMath1252.65051OpenAlexW2061744138MaRDI QIDQ714627

D. Kharzeev

Publication date: 11 October 2012

Published in: Information and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ic.2011.09.001

zbMATH Keywords

algorithmscomplementary error functionerror functionnumerical examplesroundoff errorsfloating-point arithmeticarbitrary precisionmultiple precision

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20) General theory of group and pseudogroup actions (22F05)

Related Items (5)

A unified class of penalties with the capability of producing a differentiable alternative to l₁ norm penalty ⋮ A rational-expansion-based method to compute Gabor coefficients of 2D indicator functions supported on polygonal domain ⋮ Unnamed Item ⋮ Computing integrals involved the Gaussian function with a small standard deviation ⋮ The application of real convolution for analytically evaluating Fermi-Dirac-type and Bose-Einstein-type integrals

Uses Software

• MPFR
• mctoolbox
• ARPREC
• Algorithm 524

Cites Work

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• On the Lambert \(w\) function
• MPFR
• Efficient Multiple-Precision Evaluation of Elementary Functions
• Unrestricted algorithms for elementary and special functions
• Fast evaluation of elementary mathematical functions with correctly rounded last bit
• Accuracy and Stability of Numerical Algorithms
• Pitfalls in Computation, or why a Math Book isn't Enough
• On the Number of Nonscalar Multiplications Necessary to Evaluate Polynomials

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