Theses and Dissertations - UTB/UTPA
Date of Award
8-2011
Document Type
Thesis
Degree Name
Master of Science (MS)
Department
Computer Science
First Advisor
Dr. Bin Fu
Second Advisor
Dr. Robert Schweller
Third Advisor
Dr. Matthew Patitz
Abstract
We study the hardness of some basic linear operators which involve high dimension integration or derivative. For a multivariate polynomial ��(��1, ⋯ , ����) which has format ∏ ∑ ��1, we show that there is no any factor polynomial time approximation for the integration of ��(��1, ⋯ , ����) in the unit cube [0,1] �� unless P = NP. In addition to polynomials, we extend the discussion to nonlinear function. For a trigonometric function ��(��1, ⋯ , ����) of format ∏ ∑ �������� ∗ , we show that it is #P-hard to compute derivative ����(��) (��1,⋯,����) ����1⋯������ at the origin point (��1, ⋯ , ����) = (0, ⋯ ,0). Consider the linear operator ��(��) = ∫ �� ���� (��1, ⋯ , ����)��−��(��1,⋯,����) ����1 ⋯ ������, we show that it is NP-hard to compute ��(��) for a ∏ ∑ �������� trigonometric function with the range �� = [0, ��]. And there is no any factor approximation to compute ��(��) for the ∏ ∑ �������� trigonometric function with the range �� = [0, ��].
Granting Institution
University of Texas-Pan American
Comments
Copyright 2011 Liang Ding. All Rights Reserved.
https://www.proquest.com/dissertations-theses/intractability-integration-derivative/docview/896957734/se-2?accountid=7119