计算机代数应用中的一个半逆序算法*
A Semi-Inverse Algorithm in Application of Computer Algebra
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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.Abstract: For the purpose of overcoming the difficulty of the so-called "intermediateexpression swell" in applying computer algebra, a semi-inverse algorithm is proposed.The order of seeking solutions for various problems is partly inverted, i. e., theintermediate expressions appearing in conrputation are frozen in the symbolic format first, and "unfrozen" till the formal expressions of final solulions are found out. Inthis way the overflow due to the shortage of saving space is avoided. The applicationsof the algorithm in the problems on nonllinear oscillation. dynamical optimization andinterfacial solilary waves are described. which show the effectiveness of the semi-inverse algorithm.
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