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Design of standard program library for computer algebra, and research on its efficient implementation and its applications

计算机代数标准程序库的设计、高效实现及应用研究

基本信息

批准号：
17500005
负责人：
MURAO Hirokazi
金额：
$ 2.33万
依托单位：
The University of Electro-Communications
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2007
项目状态：
已结题

项目摘要

The target of this research project is to design a standard and efficient program library for computer algebra, exploiting various techniques and technologies(SIMD, multi-core, …) for higher-performance on the commercially available processors. It started by extending the has-beein-ongoing research project and its results, including weird approach for efficiency and the use of asymptotically fast algorithms.The research results of this project include the following. (1) Summary of the behavior of fast matrix multiplication algorithm in computer algebra, and proposition of an appropriate way of its use in practice. (2) To achieve higher efficiency, the application of hyper-threading technology and multicore technology via multi-threading with shared-memory is experimented. It turned out that the memory management under shared-memory parallel processing and the relation of the levels of mathematical functionalities and the grain size of computations are the keys for multi-threaded symbolic computation. (3) For the application, we investigated the costly algorithm for plotting implicit functions and proposed a new algorithm, relating with interval arithmetics. Further investigation, in conjunction with deep understanding of interval arithmetics and with high-performance multi-thread computations can be a new research subject. (4) The last one is the experimental software for easy handling of mathematical expressions. The new Web-browser tool enjoys the latest Web-technology, and is unique.

本研究项目的目标是设计一个标准的和有效的程序库的计算机代数，利用各种技术和技术（SIMD，多核，.）在商业上可用的处理器上实现更高的性能。它首先扩展了一直在进行的研究项目及其结果，包括效率的怪异方法和渐近快速算法的使用。(1)总结了计算机代数中快速矩阵乘法算法的特点，并提出了在实际应用中的一种合适的方法。(2)为了提高系统的运行效率，通过共享内存的多线程实现了超线程技术和多核技术的应用。结果表明，共享内存并行处理下的内存管理以及数学功能层次与计算粒度的关系是多线程符号计算的关键。(3)从应用的角度出发，研究了隐函数作图的代价算法，提出了一种与区间运算有关的新算法。进一步的研究，结合对区间运算的深入理解和高性能的多线程计算，可以成为一个新的研究课题。(4)最后一个是便于处理数学表达式的实验软件。新的网络浏览器工具采用最新的网络技术，并且独一无二。