کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5773155 | 1631063 | 2017 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Minimal determinantal representations of bivariate polynomials
ترجمه فارسی عنوان
حداقل بازنمودهای تعیین کننده چندجملهای دوطبقه
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
For a square-free bivariate polynomial p of degree n we introduce a simple and fast numerical algorithm for the construction of nÃn matrices A, B, and C such that detâ¡(A+xB+yC)=p(x,y). This is the minimal size needed to represent a bivariate polynomial of degree n. Combined with a square-free factorization one can now compute nÃn matrices for any bivariate polynomial of degree n. The existence of such symmetric matrices was established by Dixon in 1902, but, up to now, no simple numerical construction has been found, even if the matrices can be nonsymmetric. Such representations may be used to efficiently numerically solve a system of two bivariate polynomials of small degree via the eigenvalues of a two-parameter eigenvalue problem. The new representation speeds up the computation considerably.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 532, 1 November 2017, Pages 550-569
Journal: Linear Algebra and its Applications - Volume 532, 1 November 2017, Pages 550-569
نویسندگان
Bor Plestenjak,