Ultra-arithmetic. I: Function data types

DOI10.1016/0378-4754(82)90045-3zbMath0493.42005OpenAlexW1998798933MaRDI QIDQ1168534

Willard L. Miranker, T. J. Rivlin, Charles L. Epstein

Publication date: 1982

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0378-4754(82)90045-3

zbMATH Keywords

minimization problemrounding errorsrounding errorFourier basisSobolev imbedding theoremdigital computerChebyshev basisultra-arithmetic

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Roundoff error (65G50) Numerical analysis in abstract spaces (65J99)

Related Items (5)

Ultra-arithmetic. II: Intervals of polynomials ⋮ Rigorous uniform approximation of D-finite functions using Chebyshev expansions ⋮ Set propagation in dynamical systems with generalised polynomial algebra and its computational complexity ⋮ Enclosing Chebyshev Expansions in Linear Time ⋮ A symbolic-numeric validation algorithm for linear ODEs with Newton-Picard method

Cites Work

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• Some new characterizations of the Chebyshev polynomials
• The Arithmetic of the Digital Computer: A New Approach

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