符号和数值混合计算

HYBRID SYMBOLIC-NUMERIC COMPUTATION

符号计算和数值计算是两种不同的解决科学和技术发展中问题的计算方法.符号计算可以得到问题精确的完备解,但是计算量大且表达形式往往十分庞大;数值计算可以快速地处理很多实际应用中的问题,但是一般只能得到近似的局部解.特别地,数值计算处理病态问题时,收敛往往较慢且容易出错.着重介绍了符号计算和数值计算之间的密切联系,以及如何运用这两大领域的最新研究成果,探索和开发符号和数值混合计算算法和软件,使之兼备符号计算的完备化和数值计算的高效性.

Symbolic computation and numeric computation are two types of computation for solving problems arising from science and engineering. Symbolic computation produces exact global solutions but is usually very expensive due to large symbolic expression; In contrast, numeric computation is fast but only produces approximate local solutions. Especially, for ill- conditioned problems, numeric algorithms converge very slowly and may return wrong results sometimes. In this paper, we emphasize the relationship between symbolic computation and numeric computation and explain how to integrate these two computations effectively to solve problems which can not be solved by using one type of computation. We also introduce some new results in the emerging area of hybrid symbolic-numeric computation.