The computation of the greatest common divisor of three bivariate Bernstein polynomials defined in a rectangular domain

This paper considers the computation of greatest common divisor (GCD) dt1,t2(x,y) three bivariate Bernstein polynomials that are defined in a rectangular domain, where t1(t2) is degree when it written as polynomial x(y) whose coefficients y(x). The Sylvester resultant matrix and its subresultant matrices used for degrees GCD. It shown there four forms these they differ their computational properties. most difficult part determination t1 t2, two methods this described. One method simple but inefficient, other reduces problem to GCD univariate polynomials, which more efficient. basis functions include binomial terms, span many orders magnitude, even moderate degrees. adverse effects wide range magnitudes significant reduction sensitivity noise obtained processed by operations before computations performed on them. Examples demonstrate theory included paper.