Isolating the real roots of the piecewise algebraic variety

Authors:
Xiaolei Zhang;Renhong Wang
Affiliations:
College of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, China;Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

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.