NDLI: A Block Projection Method for Sparse Matrices

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Arioli, Mario Duff, Iain Noailles, Joseph Ruiz, Daniel
Copyright Year	1992
Abstract	A block version of Cimminos algorithm for solving general sets of consistent sparse linear equations is described. The case of matrices in block tridiagonal form is emphasized because it is assumed that the general case can be reduced to this form by permutations. It is shown how the basic method can be accelerated by using the conjugate gradient (CG) algorithm. This acceleration is very dependent on a partitioning of the original system and several possible partitionings are discussed. Underdetermined systems corresponding to the subproblems of the partitioned system are solved using the Harwell sparse symmetric indefinite solver MA27 on an augmented system. These systems are independent and can be solved in parallel. An analysis of the iteration matrix for the conjugate gradient acceleration leads to the consideration of rather unusual and novel scalings of the matrix that alter the spectrum of the iteration matrix to reduce the number of CG iterations.The various aspects of this algorithm have been tested by runs on an eight-processor Alliant FX/80 on four block tridiagonal systems, two from fluid dynamics simulations and two from the literature. The effect of partitioning and scaling on the number of iterations and overall elapsed time for solution is studied. In all cases, an accurate solution with rapid convergence can be obtained.
Starting Page	47
Ending Page	70
Page Count	24
File Format	PDF
ISSN	01965204
DOI	10.1137/0913003
Issue Number	1
Volume Number	13
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	projection methods Iterative methods for linear systems augmented systems partitioning Overdetermined systems, pseudoinverses Parallel computation Sparse matrices block iterative methods parallel processing sparse matrices conjugate gradient preconditioning block Cimmino method
Content Type	Text
Resource Type	Article

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