Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Parallel computation: models and methods
Parallel computation: models and methods
Approximate sparsity patterns for the inverse of a matrix and preconditioning
IMACS'97 Proceedings on the on Iterative methods and preconditioners
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
The impact of high-performance computing in the solution of linear systems: trends and problems
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
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A new parallel normalized optimized approximate inverse algorithm for computing explicitly approximate inverses, is introduced for symmetric multiprocessor (SMP) systems. The parallelization of the approximate inverse has been implemented by an antidiagonal motion, in order to overcome the data dependencies. The parallel normalized explicit approximate inverses are used in conjuction with parallel normalized explicit preconditioned conjugate gradient schemes, for the efficient solution of finite element sparse linear systems. The parallel design and implementation issues of the new algorithms are discussed and the parallel performance is presented, using OpenMP. The speedups tend to the upper theoretical bounds for all cases making approximate inverse preconditioning suitable for SMP systems.