1. A numerical processing apparatus for deciding correspondence from output points in an output space of m dimensions to input points in an input space of n dimensions wherein m is smaller than n, the numerical processing apparatus comprising: a limited output point group generation unit that generates limited output points in the output space respectively corresponding to limited input points satisfying a predetermined constraint condition that is set in the input space in advance, to generate a plurality of limited pairs each consisting of a limited input point and a corresponding limited output point; and an input point element determination unit that generates an inverse mapping function from the output space onto the input space based on the plurality of limited pairs and determines at least one element of the input point satisfying the constraint condition, when an output point is given, using the inverse mapping function.