Parallel minimal norm method for tridiagonal linear systems

Dekker, Eskil; Dekker, L.

doi:10.1109/12.392854

Cited by 4 publications

(2 citation statements)

References 9 publications

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“…The matrix{vector product heavily depends on the density of the matrix and, eventually, on its particular sparsity pattern. Some interesting results on the parallelization of iterative methods for large and sparse linear systems are found in26,27,28,29].…”

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confidence: 99%

Optimal algorithms for well-conditioned nonlinear systems of equations

Bianchini

Fanelli

Gori

2001

IEEE Trans. Comput.

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We propose to solve nonlinear systems of equations by function optimization and we give an optimal algorithm which relies on a special canonical form of gradient descent. The algorithm can be applied under certain assumptions on the function to be optimized, that is an upper{bound must exist for the norm of the Hessian, whereas the norm of the gradient must be lower{bounded. Due to its intrinsic structure, the algorithm looks particularly appealing for a parallel implementation. As a particular case, more speci c results are given for linear systems. We prove that reaching a solution with degree of precision " takes n 2 k 2 log k " , being k the condition number of A and n the problem dimension. Related results hold for systems of quadratic equations, for which an estimation for the requested bounds can be devised. Finally, we report numerical results in order to establish the actual

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confidence: 99%

Optimal algorithms for well-conditioned nonlinear systems of equations

Bianchini

Fanelli

Gori

2001

IEEE Trans. Comput.

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“…The recurrence equations are used frequently on many applications like Gauss elimination, the tridiagonal matrix solver and DPCM (Differential Pulse-Code Modulation) codec, so it is very important to implement the recurrence equation solver on GPGPU systems in order to achieve a high performance [2]- [5]. Then, we modify the parallel algorithm of a recurrence equation solver (called "Pscheme") so that it is suitable for GPGPU system and we evaluate the performance comparison of our improved method (called "P-scheme/G") on GPU and CPU.…”

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confidence: 99%

Evaluation of P-Scheme/G Algorithm for Solving Recurrence Equations

Wakatani¹

2013

IJMO

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Abstract-A parallel algorithm called P-scheme/G is proposed for solving recurrence equations on GPGPU systems. This is based on P-scheme algorithm that has been originally developed for distributed memory multicomputers. In order to achieve a high performance computation on GPGPU systems, our method alleviates branch divergences by reducing the stride data accesses. We also illustrate the effectiveness of the optimal thread configuration for the recurrence equation. Our experiments with GTX 590 show that the implementation of the rearrangement using the shared memory improves the performance by 200\% to 300\% and the validity of the policy of the thread configuration is confirmed for both the constant and the non-constant parameter cases. We achieve the speedup of around 400 as a recurrence equation solver with non-constant parameters.Index Terms-CUDA, GPU, multithreading, tridiagonal matrix solver.

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