Linear approach to the least-squares multidimensional polynomial fitting

It is well known that the least-squares one-dimensional (1-D) polynomial fitting problem is linear. However, multidimensional (M-D) polynomial fitting is often treated as a nonlinear problem. This paper shows that the least-squares M-D polynomial fitting problem is also a linear problem, and proposes a linear method for solving it. Two fitting examples in the 2-D case are given to illustrate the effectiveness of the proposed method.