A scalable iterative dense linear system solver for multiple right-hand sides in data analytics
| Autor: | A. Cristiano I. Malossi, Vassilis Kalantzis, Yousef Saad, Costas Bekas, Alessandro Curioni, Efstratios Gallopoulos |
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| Rok vydání: | 2018 |
| Předmět: |
Computer Networks and Communications
ScaLAPACK Computer science Diagonal Linear system 010103 numerical & computational mathematics Positive-definite matrix Solver 01 natural sciences Computer Graphics and Computer-Aided Design Theoretical Computer Science 010101 applied mathematics Matrix (mathematics) Rate of convergence Artificial Intelligence Hardware and Architecture Conjugate gradient method 0101 mathematics Galerkin method Matrix inverse Algorithm Software Cholesky decomposition Block (data storage) |
| Zdroj: | Parallel Computing. 74:136-153 |
| ISSN: | 0167-8191 |
| DOI: | 10.1016/j.parco.2017.12.005 |
| Popis: | We describe Parallel-Projection Block Conjugate Gradient ( pp-bcg ), a distributed iterative solver for the solution of dense and symmetric positive definite linear systems with multiple right-hand sides. In particular, we focus on linear systems appearing in the context of stochastic estimation of the diagonal of the matrix inverse in Uncertainty Quantification. pp-bcg is based on the block Conjugate Gradient algorithm combined with Galerkin projections to accelerate the convergence rate of the solution process of the linear systems. Numerical experiments on massively parallel architectures illustrate the performance of the proposed scheme in terms of efficiency and convergence rate, as well as its effectiveness relative to the (block) Conjugate Gradient and the Cholesky-based ScaLAPACK solver. In particular, on a 4 rack BG/Q with up to 65,536 processor cores using dense matrices of order as high as 524,288 and 800 right-hand sides, pp-bcg can be 2x-3x faster than the aforementioned techniques. |
| Databáze: | OpenAIRE |
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