Readers interested in numerical methods and systems theory will find a significant contribution to bivariate interpolation in this paper.

Six sections and one appendix are dedicated to the subject. The first section introduces the subject, its history, and contributors to the field’s development. A recursive algorithm for computing the nth order Newton interpolating polynomial for a two-variable function is proposed in the second section. The use of divided differences for the evaluation of the coefficients of the Newton form interpolation polynomial is detailed in the third section, where an efficient algorithm is developed.

Triangular bases are used for the algorithms previously described. Using a rectangular basis, in the fourth section, the authors present a special case in which the interpolating two-variable polynomial p(x,y) has specific upper bounds on the degrees in terms of x and y. The results of a comparison of the algorithms are presented in the fifth section. It was found that the algorithms using rectangular bases are the best.

Finally, the authors apply their best interpolation algorithm for the numerical computation of the inverse of a two-variable polynomial matrix in order to obtain a fast algorithm.

By including inspired examples and adequate references in this well-structured paper, the authors fulfill their goal.