Multidimensional Algebraic Polynomial Approximation

A computational algorithm to approximate an n-dimensional function of the form F(x,y,z, ...) by an algebraic polynomial in the least square (LSQ) sense is described. The basis of this algorithm is that the n-dimensional function can be approximated by a set of polynomials in each one of the independent variables x,y,z, ... . This technique is illustrated by deriving the algebraic polynomial approximation in the LSQ sense for three-dimensional functions of the form F(x,y,z).