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用部分选主元的高斯消去法并行求解线性方程组

Portion of pivoting in parallel Gaussian elimination method for solving linear equations

中文摘要英文摘要

高斯消去法,又称高斯消元法,实际上就是我们俗称的加减消元法。数学上,高斯消去法或称高斯-约当消去法,由高斯和约当得名(很多人将高斯消去作为完整的高斯-约当消去的前半部分),它是线性代数中的一个算法,用于决定线性方程组的解,决定矩阵的秩,以及决定可逆方矩阵的逆。当用于一个矩阵时,高斯消去产生"行消去梯形形式"。用高斯消去法求解线性方程组的解是一种比较常见的解线性方程组的方法,这种方法尤其在利用计算机求解线性方程组时是更是常用。但大多数情况下都是用串行的算法来解方程组,本文介绍了利用高斯消去法并行求解线性方程组的方法。

Gaussian elimination, also calls Gauss the elimination, in fact is the elimination by addn which we are named. In mathematics, the gaussian elimination or called Gauss - approximately works as elimination, by the Gauss peace treaty, when acquires fame (many people to eliminate Gauss takes complete Gauss - when approximately eliminates the first half part), it is in a linear algebra algorithm, uses in deciding that system of linear equations's solution, decides the matrix the order, as well as decision reversible side matrix going against. When uses in a matrix, Gauss eliminates the production "the line to eliminate the trapezoidal form". With the gaussian elimination solution system of linear equations's solution is one quite common solution system of linear equations's method, this method when solves the system of linear equations especially using the computer is commonly used. But in the majority situations was solves the equation set with the serial algorithm, this article introduced used the gaussian elimination parallel solution system of linear equations's method.

刘向娇、刘佳梅

数学

高斯消去法求解线性方程组并行

Gaussian eliminationsystem of linear equationsparallel

刘向娇,刘佳梅.用部分选主元的高斯消去法并行求解线性方程组[EB/OL].(2010-11-03)[2025-08-18].http://www.paper.edu.cn/releasepaper/content/201011-62.点此复制

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