Preconditioned CG methods for sparse matrices on massively parallel machines
Parallel Computing
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
Solving Linear Systems on Vector and Shared Memory Computers
Solving Linear Systems on Vector and Shared Memory Computers
A Parallel Version of the Quasi-Minimal Residual Method, Based on Coupled Two-Term Recurrences
PARA '96 Proceedings of the Third International Workshop on Applied Parallel Computing, Industrial Computation and Optimization
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In this paper we mainly study the parallelization of the CGLS method, a basic iterative method for large and sparse least squares problems in which the conjugate gradient method is applied to solve normal equations. On modern parallel architectures its parallel performance is always limited because of the global communication required for inner products, the main bottleneck of parallel performance. In this paper, we describe a modified CGLS (MCGLS) method which improve parallel performance by assembling the results of a number of inner products collectively and by creating situations where communication can be overlapped with computation. More importantly, we also propose an improved CGLS (ICGLS) method to reduce inner product's global synchronization points to half, then significantly improve the parallel performance accordingly compared with the standard CGLS method and the MCGLS method.