کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607606 1337872 2011 11 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Multivariate splines and polytopes
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Multivariate splines and polytopes
چکیده انگلیسی

In this paper, we use multivariate splines to investigate the volume of polytopes. We first present an explicit formula for the multivariate truncated power, which can be considered as a dual version of the famous Brion’s formula for the volume of polytopes. We also prove that the integration of polynomials over polytopes can be dealt with by using the multivariate truncated power. Moreover, we show that the volume of cube slicing can be considered as the maximum value of the box spline. On the basis of this connection, we give a simple proof for Good’s conjecture, which has been settled before by probability methods.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 163, Issue 3, March 2011, Pages 377–387
نویسندگان
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