Parallel and vector conjugate gradient-like algorithms for sparse nonsymmetric linear systems
ICS '88 Proceedings of the 2nd international conference on Supercomputing
High performance preconditioning
SIAM Journal on Scientific and Statistical Computing
s-step iterative methods for symmetric linear systems
Journal of Computational and Applied Mathematics
Parallel programming with MPI
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Parallel computation: models and methods
Parallel computation: models and methods
Iterative solution of linear systems in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Parallel Programming in C with MPI and OpenMP
Parallel Programming in C with MPI and OpenMP
The Journal of Supercomputing
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A new class of parallel normalized preconditioned conjugate gradient type methods in conjunction with normalized approximate inverses algorithms, based on normalized approximate factorization procedures, for solving sparse linear systems of irregular structure, which are derived from the finite element method of a two dimensional boundary value problem, is introduced. Parallel normalized explicit preconditioned conjugate gradient - type methods for distributed memory systems based on the block - row distribution (for the vectors and the explicit approximate inverse), using Message Passing Interface (MPI) communication library, is also presented with theoretical estimates on speedups and efficiency, in order to examine the parallel behavior of these methods using normalized explicit approximate inverses as the suitable preconditioner. Collective communications have been utilized at the synchronization points and non - blocking communications have been used, where the exchanging of messages can be overlapped with computations, where applicable. Application of the methods on a two dimensional boundary value problem is discussed and numerical results are given, concerning the parallel performance in terms of speedups and efficiency.