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The gauss-huard algorithm and LU factorization

LINEAR ALGEBRA AND ITS APPLICATIONS 1998年 276卷 281-286页

作者： Hoffmann, W Univ Amsterdam Fac Math Comp Sci Phys & Astron NL-1098 SJ Amsterdam Netherlands

In this paper we analyze the gauss-huard algorithm. From a description of the algorithm in terms of matrix-vector operations we reveal a close relation between the gauss-huard algorithm and an LU factorization as cons... 详细信息

关键词： gauss-huard algorithm LU factorization

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Revisiting the gauss-huard algorithm for the Solution of Linear Systems on Graphics Accelerators 11th

Revisiting the Gauss-Huard Algorithm for the Solution of Lin...

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11th International Conference on Parallel Processing and Applied Mathematics (PPAM)

作者： Benner, Peter Ezzatti, Pablo Quintana-Orti, Enrique S. Remon, Alfredo Max Planck Inst Dynam Complex Tech Syst D-39106 Magdeburg Germany Univ Republica Inst Comp Montevideo 11300 Uruguay Univ Jaime I Dept Ingn & Ciencia Comp Castellon de La Plana 12701 Spain

ISBN: (纸本)9783319321493;9783319321486

In 1979, P. huard presented an efficient variant of the gauss-Jordan elimination for the solution of linear systems. In particular, this alternative algorithm exhibits the same computational cost as the traditional LU-based solver, and is considerably cheaper than the gauss-Jordan algorithm, but there exist no recent high performance implementations of the gauss-huard (GH) variant that allow a comparison of these approaches. In this paper we present a reliable GH solver for hybrid platforms equipped with conventional multi-core technology and a graphics processing unit (GPU). The experimental results show that the GH algorithm can beat high performance versions of the LU solver, from tuned libraries for CPU-GPU servers such as MAGMA, for problems of small to moderate scale.

关键词： Dense linear systems gauss-huard algorithm LU factorization Multi-core processors Graphics Processing Units (GPUs) High performance

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The Impact of Panel Factorization on the gauss-huard algorithm for the Solution of Linear Systems on Modern Architectures 16th

The Impact of Panel Factorization on the Gauss-Huard Algorit...

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16th International Conference on algorithms and Architectures for Parallel Processing (ICA3PP)

作者： Catalan, Sandra Ezzatti, Pablo Quintana-Orti, Enrique S. Remon, Alfredo Univ Jaime I Dep Ingn & Ciencia Compuatc Castellon de La Plana 12701 Spain Univ Republica Inst Computat Montevideo 11300 Uruguay Max Planck Inst Dynam Complex Tech Syst D-30106 Magdeburg Germany

ISBN: (纸本)9783319495835;9783319495828

The gauss-huard algorithm (the GHA) is a specialized version of gauss-Jordan elimination for the solution of linear systems that, enhanced with column pivoting, exhibits numerical stability and computational cost close to those of the conventional solver based on the LU factorization with row pivoting. Furthermore, the GHA can be formulated as a procedure rich in matrix multiplications, so that high performance can be expected on current architectures with multi-layered memories. Unfortunately, in principle the GHA does not admit the introduction of look-ahead, a technique that has been demonstrated to be rather useful to improve the performance of the LU factorization on multi-threaded platforms with high levels of hardware concurrency. In this paper we analyze the effect of this drawback on the implementation of the GHA on systems accelerated with graphics processing units (GPUs), exposing the roles of the CPU-to-GPU and single precision-to-double precision performance ratios, as well as the contribution from the operations in the algorithm's critical path.

关键词： Linear systems of equations gauss-huard algorithm LU factorization Multicore processors Graphics processing units (GPUs) Mixed precision High performance

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Solving Linear Systems on the Intel Xeon-Phi Accelerator via the gauss-huard algorithm 2nd

Solving Linear Systems on the Intel Xeon-Phi Accelerator via...

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2nd Latin American High-Performance Computing Conference (CARLA)

作者： Dufrechou, Ernesto Ezzatti, Pablo Quintana-Orti, Enrique S. Remon, Alfredo Univ Republica Inst Comp Montevideo 11300 Uruguay Univ Jaime I Dept Ingn & Ciencia Comp Castellon de La Plana 12701 Spain Max Planck Inst Dynam Complex Tech Syst D-30106 Magdeburg Germany

ISBN: (纸本)9783319269283;9783319269276

The solution of linear systems is a key operation in many scientific and engineering applications. Traditional solvers are based on the LU factorization of the coefficient matrix, and optimized implementations of this method are available in well-known dense linear algebra libraries for most hardware architectures. The gauss-huard algorithm (GHA) is a reliable and alternative method that presents a computational effort close to that of the LU-based approach. In this work we present several implementations of GHA on the Intel Xeon Phi coprocessor. The experimental results show that our solvers based in GHA represent a competitive alternative to LU-based solvers, being an appealing method for the solution of small to medium linear systems, with remarkable reductions in the time-to-solution for systems of dimension n <= 4,000.

关键词： Dense linear systems LU factorization gauss-huard algorithm Multi-core processors Xeon Phi processor High performance

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