کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
441184 691398 2013 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Resultant matrices and the computation of the degree of an approximate greatest common divisor of two inexact Bernstein basis polynomials
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر گرافیک کامپیوتری و طراحی به کمک کامپیوتر
پیش نمایش صفحه اول مقاله
Resultant matrices and the computation of the degree of an approximate greatest common divisor of two inexact Bernstein basis polynomials
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computer Aided Geometric Design - Volume 30, Issue 4, May 2013, Pages 410–429
نویسندگان
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