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 a limited output point group in the output space corresponding to a limited input point group satisfying a predetermined constraint condition set in the input space in advance; and an input point element determination unit that determines at least one element of the input point satisfying the constraint condition, when an output point is given, on the basis of the limited input point group and the generated limited output point group.