Isolating the real roots of the piecewise algebraic variety. (English) Zbl 1165.14317

Zhang, Xiaolei; Wang, Renhong

Comput. Math. Appl. 57, No. 4, 565-570 (2009).

Summary: The piecewise algebraic variety, as a set of the common zeros of multivariate splines, is a kind of generalization of the classical algebraic variety. In this paper, we present an algorithm for isolating the zeros of the zero-dimensional piecewise algebraic variety which is primarily based on the interval zeros of univariate interval polynomials. Numerical example illustrates that the proposed algorithm is flexible.

MSC:

14P10	Semialgebraic sets and related spaces
14Q99	Computational aspects in algebraic geometry

Keywords:

real root isolation; piecewise algebraic variety; semi-algebraic set; univariate interval polynomial; interval zero

Software:

ISOLATE

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