dense linear system
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2021 ◽  
Vol 293 ◽  
pp. 02013
Author(s):  
Jinmei Wang ◽  
Lizi Yin ◽  
Ke Wang

Solving dense linear systems of equations is quite time consuming and requires an efficient parallel implementation on powerful supercomputers. Du, Zheng and Wang presented some new iterative methods for linear systems [Journal of Applied Analysis and Computation, 2011, 1(3): 351-360]. This paper shows that their methods are suitable for solving dense linear system of equations, compared with the classical Jacobi and Gauss-Seidel iterative methods.


2019 ◽  
Vol 12 (04) ◽  
pp. 1950061
Author(s):  
Mohana Sundaram Muthuvalu ◽  
Emanuele Galligani ◽  
Majid Khan Majahar Ali ◽  
Jumat Sulaiman ◽  
Ramoshweu Solomon Lebelo

The main focus of the paper is to study the performance of Arithmetic Mean (AM) iterative method in solving large and nonsingular dense linear system arising from the composite 6-point closed Newton–Cotes quadrature (6-CCNC) approximation of inhomogeneous linear Fredholm integral equations of the second kind. The derivation and implementation of the method are discussed. Some numerical results are also presented.


2018 ◽  
Vol 74 ◽  
pp. 136-153
Author(s):  
Vassilis Kalantzis ◽  
A. Cristiano I. Malossi ◽  
Costas Bekas ◽  
Alessandro Curioni ◽  
Efstratios Gallopoulos ◽  
...  

Author(s):  
Juan P. Silva ◽  
Ernesto Dufrechou ◽  
Pabl Ezzatti ◽  
Enrique S. Quintana-Ortí ◽  
Alfredo Remón ◽  
...  

The high performance computing community has traditionally focused uniquely on the reduction of execution time, though in the last years, the optimization of energy consumption has become a main issue. A reduction of energy usage without a degradation of performance requires the adoption of energy-efficient hardware platforms accompanied by the development of energy-aware algorithms and computational kernels. The solution of linear systems is a key operation for many scientific and engineering problems. Its relevance has motivated an important amount of work, and consequently, it is possible to find high performance solvers for a wide variety of hardware platforms. In this work, we aim to develop a high performance and energy-efficient linear system solver. In particular, we develop two solvers for a low-power CPU-GPU platform, the NVIDIA Jetson TK1. These solvers implement the Gauss-Huard algorithm yielding an efficient usage of the target hardware as well as an efficient memory access. The experimental evaluation shows that the novel proposal reports important savings in both time and energy-consumption when compared with the state-of-the-art solvers of the platform.


Author(s):  
Babak Falsafi ◽  
Samuel Midkiff ◽  
JackB Dennis ◽  
JackB Dennis ◽  
Amol Ghoting ◽  
...  

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