Resultant matrices and the computation of the degree of an approximate greatest common divisor of two inexact Bernstein basis polynomials Original Research Article

The computation of the degree d of an approximate greatest common divisor of two Bernstein basis polynomials image and image that are noisy forms of, respectively, the exact polynomials image and image that have a non-constant common divisor is considered using the singular value decomposition of their Sylvester image and Bézout image resultant matrices. It is shown that the best estimate of d is obtained when image is postmultiplied by a diagonal matrix Q that is derived from the vectors that lie in the null space of image, where the correct value of d is defined as the degree of the greatest common divisor of the exact polynomials image and image. The computed value of d is improved further by preprocessing image and image, and examples of the computation of d using image, image and image are presented.