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Solving systems of large dense linear equations

✍ Scribed by Roger. G. Grimes

Publisher
Springer US
Year
1988
Tongue
English
Weight
371 KB
Volume
1
Category
Article
ISSN
0920-8542

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✦ Synopsis

Many mathematical models of physical phenomena lead to solving dense systems of linear equations. As the models are refined, the order of these problems increases, usually beyond the capacity of the computer to contain the problem in central memory. This paper reviews block Gaussian elimination, which can be used to solve these problems efficiently. An implementation that achieves the maximum sustainable computational rate on a wide range of computers is given. The question of how large of a problem is currently feasible is addressed.

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For an arbitrary n x n matrix A and an n Γ— 1 column vector b, we present a systolic algorithm to solve the dense linear equations Ax = b. An important consideration is that the pivot row can be changed during the execution of our systolic algorithm. The computational model consists of n linear systo