Systolic solution of linear systems over GF(p) with partial pivoting

B. Hochet, P. Quinton, Y. Robert
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引用次数: 7

Abstract

We propose two systolic architectures for the Gaussian triangularization and the Gauss-Jordan diagonalization of large dense nxn matrices over GF(p), where p is a prime number. The solution of large dense linear systems over GF(p) is the major computational step in various algorithms issued from arithmetic number theory and computer algebra. The two proposed architectures implement the elimination with partial pivoting, although the operation of the array remains purely systolic. The last section is devoted to the design and layout of a CMOS 8 by 8 Gauss-Jordan diagonalization systolic chip over GF(2).
GF(p)上具有部分旋转的线性系统的收缩解
本文提出了GF(p)上的大密度nxn矩阵的高斯三角化和高斯-乔丹对角化的两种收缩结构,其中p是素数。GF(p)上的大型密集线性系统的解是算术数论和计算机代数中各种算法的主要计算步骤。尽管阵列的操作仍然是纯粹的收缩,但这两种提出的架构实现了部分枢轴的消除。最后一节致力于在GF(2)上设计和布局CMOS 8 × 8高斯-乔丹对角化收缩芯片。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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