Research on Algorithms for Numerical Computation by Supercomputer

超级计算机数值计算算法研究

• 批准号: 61540142
• 负责人: MORI Masatake
• 金额: $ 1.02万
• 依托单位: University of Tsukuba
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1986
• 资助国家: 日本
• 起止时间: 1986 至 1987
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-61540142/
• 关键词: Supercomputer; Large scale sparse matrix; Preconditioned conjugate gradient method; SOR method; Residual polynomial; ベクトル計算; 基本関数; 残差多項式; 前処理付き共役傾斜法; 並列計算; ベクトル化

The purpose of the present project is to investigate various algorithms for numerical computation by supercomputer, in particular algorithms for large scale sparse matrices.Natori made comparisons of various numerical methods for solving a system of linear equations with large sparse matrix such as preconditioned conjugate gradient method or preconditioned conjugate residual method.In large scale linear computations one frequently modifies a subroutine of SOR method to make it suitable for vector computer. Sugihara, Oyanagi and Mori investigated the efficiency of this modification and found that it often deteriorates the convergence property of the original SOR method.Mori presented graphs of residual polynomials of CG and ICCG methods which made it possible to explain various kinds of convergence properties of those methods.Oyanagi made research on algorithms to compute basic arithmetic functions using parallel computer, in particular on the efficiency and the error of the algorithms.

本项目的目的是研究超级计算机数值计算的各种算法，特别是大规模稀疏矩阵的算法。Natori比较了求解大规模稀疏矩阵线性方程组的各种数值方法，如预条件共轭梯度法或预条件共轭残数法。在大规模线性计算中，人们经常修改SOR方法的一个子程序，使之它适用于矢量计算机。Sugihara，Oyanagi和Mori研究了这种改进的效率，发现它经常恶化原来SOR方法的收敛性。Mori给出了CG和ICCG方法的残差多项式图，这使得解释这些方法的各种收敛性成为可能。Oyanagi研究了用并行计算机计算基本算术函数的算法，特别是算法的效率和误差。

项目成果

Natori, Makoto: "BCG method and CGS method" Kokyuroku, RIMS, Kyoto University. 613. 135-143 (1987)

Natori Makoto：“BCG 方法和 CGS 方法”Kokyuroku，RIMS，京都大学。

小柳義夫: Computer Physics Communications. 42. 333-343 (1986)

小柳芳夫：计算机物理通信。42. 333-343 (1986)

名取亮: 京都大学数理解析研究所講究録. (1987)

Ryo Natori：京都大学数学科学研究所 Kokyuroku (1987)。

森正武: Proceedings of International Symposium on Numerical Analysis.

Masatake Mori：国际数值分析研讨会论文集。

小柳義夫: 情報処理. 27. 1242-1249 (1986)

小柳芳雄：信息处理。27. 1242-1249 (1986)