The Bernstein algorithm using the modified implicit Bernstein form and its GPU parallelization using CUDA
| Autor: | P. S. Dhabe, P. S. V. Nataraj |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
TheoryofComputation_MISCELLANEOUS
Polynomial 021103 operations research Strategy and Management Computation 0211 other engineering and technologies 010103 numerical & computational mathematics 02 engineering and technology Parallel computing 01 natural sciences Bernstein polynomial Set (abstract data type) CUDA 0101 mathematics General-purpose computing on graphics processing units Safety Risk Reliability and Quality Global optimization Algorithm Global optimization problem Mathematics |
| Zdroj: | International Journal of System Assurance Engineering and Management. |
| ISSN: | 0976-4348 0975-6809 |
| DOI: | 10.1007/s13198-017-0673-x |
| Popis: | In this paper, we propose a Modified Implicit Bernstein Form (MIBF) for computing the Bernstein coefficients of a polynomial. The MIBF avoids several redundant computations in Smith’s Implicit Bernstein Form (IBF) (Smith in J Glob Optim 43:445–458, 2009). Based on the MIBF, we then propose a serial (or CPU based) Bernstein Algorithm for polynomial global optimization. On a set of test problems, the proposed Bernstein Algorithm is about 1.8 times faster than the one based on IBF in Dhabe and Nataraj (Int J Syst Assur Eng Manag, 2017). To obtain further speedups, we next propose a GPU parallel optimization algorithm based on the MIBF, and obtain speedups of up to 44 times with 97% reductions in computations over the serial version. Thus, we recommend the GPU parallel Bernstein algorithm based on the proposed MIBF form for solving polynomial global optimization problems. |
| Databáze: | OpenAIRE |
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