n维单纯形上多项式的积分

2019 Federated Conference on Computer Science and Information Systems (FedCSIS) Pub Date : 2019-09-26 DOI:10.15439/2019F16

A. Rouigueb, M. Maiza, Abderahmane Tkourt, Imed Cherchour

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引用次数: 2

摘要

在维数为n的一般单纯形上对任意D次多项式函数f进行积分，目前已知当D和n允许变化时是np困难的，但当D或n固定时则是时间多项式。本文给出了一种计算该积分精确值的有效算法。当D或n固定时，所提出的算法具有时间多项式复杂度，并且当D和n的值小于10时，使用广泛使用的标准计算器(如桌面)需要合理的时间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Integration of Polynomials over n-Dimensional Simplices

Integrating an arbitrary polynomial function f of degree D over a general simplex in dimension n is well-known in the state of the art to be NP-hard when D and n are allowed to vary, but it is time-polynomial when D or n are fixed. This paper presents an efficient algorithm to compute the exact value of this integral. The proposed algorithm has a time-polynomial complexity when D or n are fixed, and it requires a reasonable time when the values of D and n are less than 10 using widely available standard calculators such as desktops.

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来源期刊

2019 Federated Conference on Computer Science and Information Systems (FedCSIS)

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