Abstract
Linear Equations Systems may appear as modeling result of many problems in mathematics, engineering and computer science. The Bi-Conjugate Gradient Stabilized (BiCGStab) method is an iterative method used for solving linear systems, specially the sparse and large ones. In this context, this paper proposes a parallel implementation of the BiCGStab method for solving large linear systems. The proposed implementation uses a Graphics Processing Unit (GPU) through the CUDA-Matlab integration, in which the method operations are performed in the processing cores of the GPU by the Matlab built-in functions. Such implementation aims to provide a high computational performance in relation to its sequential implementation. In addition, we compare the BiCGStab computational performance with an implementation of the Hybrid Bi-Conjugate Gradient Stabilized (BiCGStab(2)) method, recently proposed by the author in the solution of random linear systems with varying sizes. The results showed that the parallelized BiCGStab is more efficient in solving the treated systems. It was possible to obtain gains of computational efficiency of approximately 5x in relation to the sequential implementation of the BiCGStab. Compared with the BiCGStab(2) the parallelized BiCGStab was on average 2x faster.
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