scholarly journals The monotone convergence of the two-stage iterative method for solving large sparse systems of linear equations

1997 ◽  
Vol 10 (1) ◽  
pp. 113-117 ◽  
Author(s):  
Zhong-Zhi Bai ◽  
De-Ren Wang
Keyword(s):  
Iterative Method ◽  
Linear Equations ◽  
Monotone Convergence ◽  
Two Stage ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Large Sparse Systems

scholarly journals A nested decomposition algorithm for parallel computations of very large sparse systems

1995 ◽  
Vol 1 (1) ◽  
pp. 41-57 ◽  
Author(s):  
D. D. Šiljak ◽  
A. I. Zečević
Keyword(s):  
Parallel Computation ◽  
Linear Equations ◽  
Parallel Computations ◽  
Decomposition Algorithm ◽  
Parallel Solution ◽  
Engineering Problems ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Block Diagonal ◽  
Large Sparse Systems

In this paper we present a generalization of the balanced border block diagonal (BBD) decomposition algorithm, which was developed for the parallel computation of sparse systems of linear equations. The efficiency of the new procedure is substantially higher, and it extends the applicability of the BBD decomposition to extremely large problems. Examples of the decomposition are provided for matrices as large as250,000×250,000, and its performance is compared to other sparse decompositions. Applications to the parallel solution of sparse systems are discussed for a variety of engineering problems.

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