Journal Article10.1016/0378-4754(82)90045-3
Ultra-arithmetic I: Function data types
29
TL;DR: The digital computer is lifted from aSetting corresponding to the real numbers to a setting corresponding to function spaces, and the algorithms of ultra-arithmetic are given in an explicitly implementable form for the cases both of the Fourier basis and the Chebyshev basis.
read more
About: This article is published in Mathematics and Computers in Simulation. The article was published on 01 Feb 1982. The article focuses on the topics: Basis function & Rounding.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
•Dissertation
Rigorous Polynomial Approximations and Applications
Mioara Maria Joldes
- 26 Sep 2011
TL;DR: Several applications are presented: one from standard functions implementation in mathematical libraries (libm), another regarding the computation of Chebyshev series expansions solutions of linear ODEs with polynomial coefficients, and an automatic process for function evaluation with guaranteed accuracy in reconfigurable hardware.
•Dissertation
Autour de l'évaluation numérique des fonctions D-finies
Marc Mezzarobba
- 27 Oct 2011
TL;DR: In this paper, the authors explore trois grandes directions, i.e., the majoration des coefficients des developpements en serie of fonctions D-finies, the mise en pratique de l'algorithme "bit burst" de Chudnovsky et.
31
Set propagation in dynamical systems with generalised polynomial algebra and its computational complexity
TL;DR: The paper first introduces the concept of generalised polynomial algebra and its use to propagate sets through dynamical systems and its time complexity is analyzed and compares it against the time complexity of a non-intrusive counterpart.
29
•Book Chapter
An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra
Annalisa Riccardi,Chiara Tardioli,Massimiliano Vasile +2 more
- 13 Aug 2015
TL;DR: In this paper, an intrusive approach to propagate uncertainty in orbital mechanics is presented based on an expansion of the uncertain quantities in Tchebicheff series and a propagation through the dynamics using a generalised polynomial algebra.
23
Ultra-arithmetic II: intervals of polynomials
TL;DR: In this article, a calculus for functions which is performable on a digital computer is presented, where the operations of addition, subtraction, multiplication, division, integration and differentiation for intervals of polynomials are defined and studied.
22
References
•Book
Computer arithmetic in theory and practice
Ulrich Kulisch,Willard L. Miranker +1 more
- 01 Jan 1981
542
An Introduction to the Approximation of Functions
TL;DR: In this article, an Introduction to the Approximation of Functions is presented, which is based on the idea of approximating functions by approximating approximations of functions with functions.
137
Ultra-arithmetic II: intervals of polynomials
TL;DR: In this article, a calculus for functions which is performable on a digital computer is presented, where the operations of addition, subtraction, multiplication, division, integration and differentiation for intervals of polynomials are defined and studied.
22
Related Papers (5)
Theodore J. Rivlin
- 01 Jan 1974
Ramon E. Moore
- 01 Jan 1987
L B Rall
- 01 Mar 1986
Lloyd N. Trefethen
- 03 Jan 2013