• 论文 •

### 关于带状线性方程组的并行求解

1. 华中工学院
• 出版日期:1988-02-20 发布日期:1988-02-20

### ON THE PARALLEL SOLUTION OF A BANDED LINEAR SYSTEM OF EQUATIONS

1. Lu Yi-jun Huazhong Unversity of Science and Technolog
• Online:1988-02-20 Published:1988-02-20
1979年,D.Evans和M.Hatzopoulos首次提出了并行求解线性代数方程组的QIF方法(简称QIF1)。随后,D.Evans与其同事在这方面做了一系列工作,其中包括QIF1的各种变形、关于QIF方法的稳定性问题以及将这种方法应用于对称正定和带状线代数方程组的并行求解等等。值得指出的是,D.Evans等在文献[3]中对QIF2提出了一种有效的并行执行技术,称为NQIF2方法,并用它来求解带状线性方程组,得到了有意义的结果。本文将作者在[4]中提出的QIF2方法的一种并行化技术应用于带状线性方程组的并行求解,得到了比文[3]更好的结果。
In this paper, a new parallel technique of NQIF2 method is applied to the parallel solu-tion of a banded system of linear equations. The conclusion of [3] is improved. This methodis P+2(-1)~n time steps faster than that of [3] with an equal number of processors. Themethod is suitable for use of a parallel computer of SIMD type.
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 [1] D. J. Evans, M. Hatzopoulos, A parallel 1inear system solvcr, lntern. J. Comp. Math., 7(1979) , 227． --238． [2] D. J. Evans, A. Hadjidimos. A modificatiall of the quadrant interlocking factorisation parallel method, Intern. J. Comp. Math., 8(1980) , 149--166． [3] D. J. Evans, A. Hadjidimos, D. Noutsos, The parallel solution of banded linear equations by the newquadrant interlocking factorisation (Q. I. F) method, Intern. J. Comp. Math.. 9(1981) , 151--161． [4] 陆益君,并行WZ分解,华中工学院学报,将发表. [5] J. Shanehcbi, D. Evans, New variants of the quadrant interlocking factorization (QIF) method, CONPAR 81 Conference, Lecture Notes in Computer Science Ⅲ, Nuremberg (W. Handler. ed.). Springer-Vcrlag, Berlin. 493--507． [6] J. Shanehchi. D. Evans, Further analysis of tbe QIF method. Intern. J. Comp. Math., 11(1982) , 143--154．
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