English

A new algebraic and arithmetic framework for interval computations

Numerical Analysis 2011-07-20 v1 Numerical Analysis

Abstract

In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to build all algebraic operations and functions on intervals. This will avoid completely the wrapping effects and data dependance. Some simple applications for matrix eigenvalues calculations, inversion of symmetric matrices and finally optimization are exhibited in the object-oriented programming language python.

Keywords

Cite

@article{arxiv.1107.3667,
  title  = {A new algebraic and arithmetic framework for interval computations},
  author = {Nicolas Goze and Michel Goze and Abdel Kenoufi and Elisabeth Remm},
  journal= {arXiv preprint arXiv:1107.3667},
  year   = {2011}
}

Comments

23 pages, 9 figures

R2 v1 2026-06-21T18:38:46.075Z