Research on Algorithms for Numerical Computation by Supercomputer

本项目的目的是研究各种超级计算机数值计算算法，特别是大规模稀疏矩阵的算法。Natori比较了求解具有大稀疏矩阵的线性方程组的各种数值方法，如预条件共轭梯度法和预条件共轭残差法。在大规模的线性计算中，人们经常修改SOR方法的子程序，使其适用于向量计算机。Sugihara， Oyanagi和Mori研究了这种改进的效率，发现它经常会降低原始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。

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.