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Real Solving of Elementary-Algebraic Systems

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Abstract

In this paper we present a new method for enclosing all the real roots in a bounded box of a system of n elementary-algebraic equations depending on n variables. This system is denoted by h(x)=P(x,f 1(x 1),...,f k (x 1),f 1(x 2),...,f k (x n )), where x=(x 1,x 2,...,x n ) ∈ R n, P is a system of polynomials depending on n+kn variables and the univariate functions f i are “simple”. This method arises from the exclusion method of Dedieu and Yakoubsohn. We provide both a theoretical complexity bound and some numerical experiments.

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  1. Université Joseph Fourier, LMC-IMAG, 51 rue des mathématiques, BP 53, 38041, Grenoble Cedex, France

    Aude Maignan

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  1. Aude Maignan
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Maignan, A. Real Solving of Elementary-Algebraic Systems. Numerical Algorithms 27, 153–167 (2001). https://doi.org/10.1023/A:1011881613933

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