Recently a simple algorithm was presented by the first author which enables one to successively compute the transformation matrix of various order for the general 1-D to 1-D polynomial transformation. This letter extends the result to the general 1-D to 2-D polynomial transformation. It is also shown that the matrix obtained can be used for the 2-D to 2-D polynomial transformation as well.

In many engineering problems it is required to convert a polynomial into another polynomial through a transformation. Due to its wide range of applications, the polynomial transformation has received much attention and many techniques have been developed to compute the coefficients of a transformed polynomial from those of an original polynomial. In this letter a new result is presented concerning the transformation matrix for arbitrary polynomial transformation. A simple algorithm is obtained which enables one to successively compute transformation matrices of various order.