Interval iterative algorithm for computing the piecewise algebraic variety

As the set of the common zeros of the multivariate splines, the piecewise algebraic variety is a kind of generalization of the classical algebraic variety. In this paper, we discuss the computation problem of the piecewise algebraic variety. The approach presented here is the interval iterative algorithm by introducing the concept of ε-deviation solutions. Meanwhile, we present a simple method to evaluate the bound on the value of the derivative of the function on a given region.