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稀疏对称高斯消去法的两个算法

郑家栋   

  1. 上海计算技术研究所
  • 出版日期:1981-01-20 发布日期:1981-01-20

郑家栋. 稀疏对称高斯消去法的两个算法[J]. 数值计算与计算机应用, 1981, 2(1): 1-7.

TWO ALGORITHMS OF SPARSE SYMMETRIC GAUSSIAN ELIMINATION

  1. Zheng Jia-dong Shanghai Computing Technical Institute
  • Online:1981-01-20 Published:1981-01-20
设A是对称正定的稀疏矩阵,我们用高斯消去法解方程组: Ax=b.(1)当A是带形矩阵时,一般可用一维存贮的变带宽算法求解.但在许多实际问题中,例如电网络问题及某些有限元问题,出现的稀疏矩阵不具有带形结构,而是根据存贮量或运算量优化的某种准则,排列矩阵各行所产生的具有随机分布稀疏结构的矩阵.本文主要讨论当A具有这种稀疏结构时,如何用对称高斯消去法结合上三角按行索引存贮技术去解
In this paper, some properties of the sparse symmetric Gaussian elimination methodare proved. On the basis of them, two algorithms that apply the indexing storage techni-que by rows are presented. The estimate of arithmetie operation which is used to takeout nonzero elements of the upper triangular matrix by columns is of the order O(n).Some technical problems concerning these algorithms are discussed.
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[1] R. P. Tewarson, Sparse matrices, Academic Press, New York and London. 1973.
[2] 华伯浩,郑家栋,稀疏矩阵的存储量优化算法,未发表.
[3] H. G. Jensen, G. A. Parks, J. Struct. Div. ASCE, 96(1970) , 49-64.
[4] F. G. Gustavson, Some basic techniques for solving sparse systems of linear equations, in "Sparse matrices and their applications" (Rose D. J. eds.), 1972.
[5] S. C. Eisenstat, M. H. Schultz, A. H. Sherman, Efficient implementation of sparse symmetric Gaussian elimination, in. "Advances in computer methods for PDE". (R. Vichnevetsty ed.), 1975.
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