Multivariable polynomial processing — Applications to interpolation

A data-structure suitable for multivariable polynomial processing is introduced. Using this data-structure, arithmetic algorithms are described for addition, subtraction and multiplication of multivariable polynomials; also algorithms are described for forming the inner product and tensor product of vectors, whose components are multivariable polynomials. Application of these algorithms. for multivariable cardinal spline approximation is described in detail.