权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Computer Algebra and Supercomputing

计算机代数和超级计算

基本信息

批准号：
05680266
负责人：
MURAO Hirokazu
金额：
$ 1.28万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1994
项目状态：
已结题

项目摘要

The overall subject of this research project is the application of supercomputers to computational algebra. The major research results are described briefly in the following.・A new modular algorithm which uses the Chinese remainder algorithm for sparse multivariate polynomial interpolation is developed, which determines unknown polynomials from their numeric values produced by efficient data-parallel processing on supercomputers. Also, its brief analysis and comparison with other algorithms are done. To evaluate its practical efficiency, the algorithm was fully implemented and tested in REDUCE,and the effort of its parallelization using C and KLIC,was made.・The new algorithm, recently developed by the investigator, for solving a system of algebraic equations was implemented on Risa/Asir, to clarify problems and appropriate methods to be used, in applying vector or parallel processing to the algorithm. It turned out that in the case of large-scale systems of equations, the computing met … More hod considered suffers from a very large amount of data to be transferred between a computer algebra system and a supercomputer each other, and therefore, requires an efficient device for interprocess communication. In this experiment, the Grobner-basis package of Risa/Asir was much improved to become the most efficient package in the world, enabling to perform maximal-scale computations.・Various algorithms for polynomial factorization are investigated theoretically and empirically. The significant findings of the experiment with a supercomputer are the facts that vector processing is substantially effective, and that among others, the Zassenhaus algorithm is generally most efficient and useful. The vectorized programs run so fast that they can factor polynomials of such high degrees as having never been tried, within a reasonable amount of time. Further investigation has been being continued to clarify how high-degree polynomial we can factorize using the state-of-the-art supercomputers. This has led to a deeper understanding of the algorithms, and brought a new algorithm.・The mechanism for network-transparent interprocess communication in Risa/Asir was slightly extended, and it was tested and evaluated very briefly, for its future use or generalization in combining the computer algebra system and supercomputing environments. Less

这个研究项目的总体主题是超级计算机在计算代数中的应用。主要研究成果简述如下。·开发了一种新的模块化算法，该算法使用中国剩余算法进行稀疏多元多项式插值，从超级计算机上高效的数据并行处理产生的数值中确定未知多项式。并与其他算法进行了简要的分析和比较。为了评估其实际效率，在REDUCE中对该算法进行了全面的实现和测试，并使用C语言和KLIC进行了并行化。研究者最近开发的用于求解代数方程组的新算法在Risa/Asir上实现，以澄清问题和适当的方法，将向量或并行处理应用于算法。结果表明，在大规模方程组的情况下，计算机代数系统和超级计算机之间需要传输非常大量的数据，因此需要一种高效的进程间通信设备。在这个实验中，Risa/Asir的grobner基础包得到了很大的改进，成为世界上最高效的包，能够执行最大规模的计算。·对多项式分解的各种算法进行了理论和经验研究。超级计算机实验的重要发现是矢量处理非常有效，而在其他算法中，Zassenhaus算法通常是最有效和有用的。向量化程序运行得如此之快，以至于它们可以在合理的时间内对从未尝试过的高阶多项式进行分解。进一步的研究还在继续，以澄清我们如何使用最先进的超级计算机来分解高阶多项式。这使得人们对算法有了更深入的了解，并带来了新的算法。·对Risa/Asir中网络透明进程间通信的机制进行了稍微扩展，并对其进行了非常简短的测试和评估，以便将来在计算机代数系统和超级计算环境的结合中使用或推广。少