Parallel implementation of the block conjugate gradient algorithm
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A scalable iterative dense linear system solver for multiple right-hand sides in data analytics
2018, Parallel ComputingCitation Excerpt :The latter represents a challenging task, especially given the increasing gap between the cost of elementary arithmetic and communication operations. Therefore, it is not surprising that in spite of the sizeable literature on multiple right-hand side solvers, there is relatively little on parallel methods [1,7,18,21,31,36,38,40] and even less [8,18,33] for problems that satisfy the stated assumptions (in particular dense and SPD matrices) holding in the application under consideration in this paper. The literature on parallel solvers is more extensive for the nonsymmetric case, see e.g. [23,32,35,42,52].
Block Conjugate Gradient algorithms for least squares problems
2017, Journal of Computational and Applied MathematicsImproving performance of sparse matrix dense matrix multiplication on large-scale parallel systems
2016, Parallel ComputingCitation Excerpt :The practical benefits of block methods have been emphasized in several studies. These studies either focus on the block versions of certain solvers (i.e., conjugate gradient variants) which address multiple linear systems [1–4], or the block methods for eigenvalue problems, such as block Lanczos [5] and block Arnoldi [6]. The column dimension of X and Y in block methods is usually very small compared to that of A [7].
Efficient parallel implementations of finite element methods based on the conjugate gradient method
2003, Applied Mathematics and ComputationDevelopments and trends in the parallel solution of linear systems
1999, Parallel Computing
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This work was supported by the Air Force Office of Scientific Research under Grant AFOSR-82-0078.