A Hybrid Chebyshev Krylov Subspace Algorithm for Solving Nonsymmetric Systems of Linear Equations

1986 ◽  
Vol 7 (3) ◽  
pp. 840-855 ◽  
Author(s):  
Howard C. Elman ◽  
Youcef Saad ◽  
Paul E. Saylor
Keyword(s):  
Krylov Subspace ◽  
Linear Equations ◽  
Subspace Algorithm ◽  
Systems Of Linear Equations ◽  
Nonsymmetric Systems

scholarly journals Accelerating advanced preconditioning methods on hybrid architectures

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Ernesto Dufrechou
Keyword(s):  
Linear Systems ◽  
Large Scale ◽  
Krylov Subspace ◽  
Linear Equations ◽  
Memory Systems ◽  
Sparse Linear Systems ◽  
Data Parallel ◽  
Systems Of Linear Equations ◽  
Sparse Systems ◽  
Computational Bottleneck

Many problems, in diverse areas of science and engineering, involve the solution of largescale sparse systems of linear equations. In most of these scenarios, they are also a computational bottleneck, and therefore their efficient solution on parallel architectureshas motivated a tremendous volume of research.This dissertation targets the use of GPUs to enhance the performance of the solution of sparse linear systems using iterative methods complemented with state-of-the-art preconditioned techniques. In particular, we study ILUPACK, a package for the solution of sparse linear systems via Krylov subspace methods that relies on a modern inverse-based multilevel ILU (incomplete LU) preconditioning technique.We present new data-parallel versions of the preconditioner and the most important solvers contained in the package that significantly improve its performance without affecting its accuracy. Additionally we enhance existing task-parallel versions of ILUPACK for shared- and distributed-memory systems with the inclusion of GPU acceleration. The results obtained show a sensible reduction in the runtime of the methods, as well as the possibility of addressing large-scale problems efficiently.

Variational Iterative Methods for Nonsymmetric Systems of Linear Equations

1983 ◽  
Vol 20 (2) ◽  
pp. 345-357 ◽  
Author(s):  
Stanley C. Eisenstat ◽  
Howard C. Elman ◽  
Martin H. Schultz
Keyword(s):  
Iterative Methods ◽  
Linear Equations ◽  
Systems Of Linear Equations ◽  
Nonsymmetric Systems
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