A NOVEL PARTITIONING METHOD FOR ACCELERATING THE BLOCK CIMMINO ALGORITHM

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Date

2018-01-01

Author

Torun, F. Sukru
Manguoğlu, Murat
Aykanat, Cevdet

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We propose a novel block-row partitioning method in order to improve the convergence rate of the block Cimmino algorithm for solving general sparse linear systems of equations. The convergence rate of the block Cimmino algorithm depends on the orthogonality among the block rows obtained by the partitioning method. The proposed method takes numerical orthogonality among block rows into account by proposing a row inner-product graph model of the coefficient matrix. In the graph partitioning formulation defined on this graph model, the partitioning objective of minimizing the cutsize directly corresponds to minimizing the sum of interblock inner products between block rows thus leading to an improvement in the eigenvalue spectrum of the iteration matrix. This in turn leads to a significant reduction in the number of iterations required for convergence. Extensive experiments conducted on a large set of matrices confirm the validity of the proposed method against a state-of-the-art method.

Subject Keywords

Row projection methods, Block Cimmino algorithm, Krylov subspace methods, Row inner-product graph, Graph partitioning

URI

https://hdl.handle.net/11511/38983

Journal

SIAM JOURNAL ON SCIENTIFIC COMPUTING

DOI

https://doi.org/10.1137/18m1166407

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Department of Computer Engineering, Article

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Citation Formats

F. S. Torun, M. Manguoğlu, and C. Aykanat, “A NOVEL PARTITIONING METHOD FOR ACCELERATING THE BLOCK CIMMINO ALGORITHM,” SIAM JOURNAL ON SCIENTIFIC COMPUTING, pp. 0–0, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38983.