| 计算机代数应用中的一个半逆序算法* |
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| 引用本文： | 戴世强,臧宏鸣.计算机代数应用中的一个半逆序算法*[J].应用数学和力学,1997,18(2):105-111. |
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| 作者姓名： | 戴世强 臧宏鸣 |
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| 作者单位： | 上海大学, 上海市应用数学和力学研究所, 上海 200072 |
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| 基金项目： | 国家自然科学基金，上海市自然科学基金，上海市高教局博士点基金 |
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| 摘 要： | 为了克服计算机代数应用中出现的"中间表达式爆炸"的困难,本文提出一种半逆序算法,将中间表达式在运算过程中以符号形式冻结起来,到求解的最后阶段予以解冻,从而避免了因存贮空间不足而导致的溢出.文中简述了该算法在非线性振动、冷却塔动力优化和非线性水波问题中的应用,证实了算法的有效性.
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| 关 键 词： | 计算机代数 符号运算 中间表达式爆炸 摄动法 非线性分析 |
| 收稿时间： | 1995-10-11 |
A Semi-Inverse Algorithm in Application of Computer Algebra |
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| Dai Shiqiang, Zang Hongming.A Semi-Inverse Algorithm in Application of Computer Algebra[J].Applied Mathematics and Mechanics,1997,18(2):105-111. |
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| Authors: | Dai Shiqiang Zang Hongming |
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| Institution: | Shanghai Institute of Applied Mathematics and Mechanics, ShanghaiUniversity, Shanghai 200072, P. R. China |
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| Abstract: | For the purpose of overcoming the difficulty of the so-called "intermediate expression swell" in applying computer algebra, a semi-inverse algorithm is proposed. The order of seeking solutions for various problems is partly inverted, i.e. the intermediate expressions appearing in computation are "frozen'"in the symbolic form at first, and "unfrozen" till the formal expressions of final, solutions are found out. In this way, the overflow due to the shortage of saving space is avoided. The applications of the algorithm in the problems on nonlinear oscillation, dynamical optimization and interfacial solitary waves are described,which shows the effectiveness of the semi-inverse algorithm. |
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| Keywords: | computer algebra symbolic computation intermediate expression swell perturbation method nonlinear analysis |
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