A new algebraic and arithmetic framework for interval computations

Details A new algebraic and arithmetic framework for interval computations A new algebraic and arithmetic framework for interval computations

2011-07-19

arxiv.org/abs/1107.3667v1

Computer Science

Numerical Analysis

23 pages, 9 figures

Scientific paper

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.

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