Determining the parametrization of the curve is a fundamental problem in approximation and interpolation. The goal of this paper is to develop an accurate and robust algorithm for the minimum zone problems. In this paper, we use an interval bias adaptive linear neural network structure together with an appropriate cost function and the least mean squares learning algorithm to carry out the interval regression analysis. Through appropriate choice of the output function of the input neuron, the interval polynomial regression use of a neural network (IPRNN) method developed in this paper is applicable to many problems (interval algebraic polynomial approximation, evaluation of straightness, roundness and ellipticity and so on). Generally, these problems have complicated constraints and the LSQ method cannot be used.
