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題名: | Decomposing 40 Billion Integers by Four Tetrahedral Numbers |
作者: | Chou, Chung-Chiang;Deng, Yuefan |
貢獻者: | 數學系 |
關鍵詞: | Asymptotic form;Parallel computing;Waring's problem |
日期: | 1997-04
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上傳時間: | 2013-03-12T04:07:55Z
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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 |
顯示於類別: | [數學系] 期刊論文
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