密行列専用計算機GENERAL - 1の開発  [in Japanese] A special - purpose computer for solving a dense matrix based on the Gaussian elimination algorithm : GENERAL - 1  [in Japanese]

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Abstract

係数行列が密であるn元連立一次方程式を高速に解くための専用計算機について述べる。密行列を解く際にはガウスの消去法が通常使われる。ガウスの消去法の演算量は、行列の大きさnの3乗に比例する。そのため、大規模密行列を解くためには、高い計算能力が要求される。ガウスの消去法において、n^3のオーダーの演算量を要するのは前進消去の制限三項演算または内積演算のみである。本論文では、この内積演算のみを専用計算横で解き、残りの演算を既存の汎用機で行なうシステムについて論ずる。現在、この密行列専用計算機の試作機GENERAL-1を製作中である。GENERAL-1のピーク性能は80Mflops(倍精度計算時)であり、n=1000の連立1次方程式を約20秒で解ける。We describe a special-purpose computer for solving a set of linear equations. We usually use Gaussian elimination algorithm to solve a dense matrix. In this method the number of operations to solve the matrix is proportional to a cube of the matrix size. Therefore, we require a large amount of computational power for large-scale problems. However, the calculations are dominated by sum-of-products operations in the forward eliminations. In the paper, we propose a system the consists of a special-purpose computer and a host computer. The special-purpose computer does only sum-of-products operations, and the host computer does all the other operations. We are developing an experimental machine of GENERAL-1 (Gaussian ElimiNation mEthod paRALlel machine). It will have a peak performance of 80Mflops and will solve a matrix of n=1000 in 20 seconds.

We describe a special-purpose computer for solving a set of linear equations. We usually use Gaussian elimination algorithm to solve a dense matrix. In this method the number of operations to solve the matrix is proportional to a cube of the matrix size. Therefore, we require a large amount of computational power for large-scale problems. However, the calculations are dominated by sum-of-products operations in the forward eliminations. In the paper, we propose a system that consists of a special-purpose computer and a host computer. The special-purpose computer does only sum-of-products operations, and the host computer does all the other operations. We are developing an experimental machine of GENERAL-1 (Gaussian ElimiNation mEthod paRALlel machine). It will have a peak performance of 80Mflops and will solve a matrix of n=1000 in 20 seconds.

Journal

  • IPSJ SIG Notes

    IPSJ SIG Notes 1994(29(1994-ARC-111)), 65-72, 1995-03-10

    Information Processing Society of Japan (IPSJ)

References:  8

Codes

  • NII Article ID (NAID)
    110002775396
  • NII NACSIS-CAT ID (NCID)
    AN10096105
  • Text Lang
    JPN
  • Article Type
    Technical Report
  • ISSN
    09196072
  • Data Source
    CJP  NII-ELS  IPSJ 
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