کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
441184 | 691398 | 2013 | 20 صفحه PDF | دانلود رایگان |

The computation of the degree d of an approximate greatest common divisor of two Bernstein basis polynomials f(y)f(y) and g(y)g(y) that are noisy forms of, respectively, the exact polynomials fˆ(y) and gˆ(y) that have a non-constant common divisor is considered using the singular value decomposition of their Sylvester S(f,g)S(f,g) and Bézout B(f,g)B(f,g) resultant matrices. It is shown that the best estimate of d is obtained when S(f,g)S(f,g) is postmultiplied by a diagonal matrix Q that is derived from the vectors that lie in the null space of S(f,g)S(f,g), where the correct value of d is defined as the degree of the greatest common divisor of the exact polynomials fˆ(y) and gˆ(y). The computed value of d is improved further by preprocessing f(y)f(y) and g(y)g(y), and examples of the computation of d using S(f,g)S(f,g), S(f,g)QS(f,g)Q and B(f,g)B(f,g) are presented.
► Resultant matrices are used to determine the degree of the approximate greatest common divisor of two Bernstein basis polynomials.
► Preprocessing operations are applied to the polynomials before the resultant matrices are computed.
► Better answers are obtained when a modified form of the Sylvester resultant matrix is used.
► This matrix yields better results than the Bézout resultant matrix.
► An explanation for these improved results is given.
Journal: Computer Aided Geometric Design - Volume 30, Issue 4, May 2013, Pages 410–429