Abstract
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Article Information:
A Generalized Permanent Estimator and its Application in Computing Multi-Homogeneous Bézout Number
Hassan M.S. Bawazir, Ali Abd Rahman and Nor’aini binti Aris
Corresponding Author: Hassan M.S. Bawazir
Submitted: April 25, 2012
Accepted: May 13, 2012
Published: December 01, 2012 |
Abstract:
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The permanent of a matrix has many applications in many fields. Its computation is #P-complete.
The computation of exact permanent large-scale matrices is very costly in terms of memory and time. There
is a real need for an efficient method to deal well with such situations. This study designs a general algorithm
for estimating the permanents of the complex square or non-square matrices. We prove that the Multi-
Homogeneous Bézout Number (MHBN) can be estimated efficiently using the new algorithm. Further, a
proposition that provides some analytic results is presented and proved. The analytic results show the
effectiveness and the efficiency of our algorithm over some recent methods. Furthermore, with the new
algorithm we can control the accuracy as we need. A large amount of numerical results are presented in this
study. By applying the algorithm that estimates MHBN we extend the applicability of the algorithm.
Key words: Multi-homogeneous bézout number, permanent, polynomial system, random path, , ,
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Cite this Reference:
Hassan M.S. Bawazir, Ali Abd Rahman and Nor’aini binti Aris, . A Generalized Permanent Estimator and its Application in Computing Multi-Homogeneous Bézout Number. Research Journal of Applied Sciences, Engineering and Technology, (23): 5206-5211.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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