National Changhua University of Education Institutional Repository : Item 987654321/15816
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题名: Decomposing 40 Billion Integers by Four Tetrahedral Numbers
作者: Chou, Chung-Chiang;Deng, Yuefan
贡献者: 數學系
关键词: Asymptotic form;Parallel computing;Waring's problem
日期: 1997-04
上传时间: 2013-03-12T04:07:55Z
出版者: American Mathematical Society
摘要: Based upon a computer search performed on a massively parallel supercomputer, we found that any integer n less than 40 billion (40B) but greater than 343, 867 can be written as a sum of four or fewer tetrahedral numbers. This result has established a new upper bound for a conjecture compared to an older one, 1B, obtained a year earlier. It also gives more accurate asymptotic forms for partitioning. All this improvement is a direct result of algorithmic advances in efficient memory and cpu utilizations. The heuristic complexity of the new algorithm is O(n) compared with that of the old, O(n5/3 log n).
關聯: Mathematics of Computation, 66(218): 893-901
显示于类别:[數學系] 期刊論文


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