Optimal parallel algorithms for solving tridiagonal linear systems

1997 ◽  
pp. 700-709 ◽  
Author(s):  
Eunice E. Santos
Keyword(s):  
Parallel Algorithms ◽  
Linear Systems

Parallel algorithms of the Purcell method for direct solution of linear systems

2002 ◽  
Vol 28 (9) ◽  
pp. 1275-1291 ◽  
Author(s):  
Ke Chen ◽  
Choi H. Lai
Keyword(s):  
Parallel Algorithms ◽  
Linear Systems ◽  
Direct Solution

Book Reviews

1994 ◽  
Vol 208 (2) ◽  
pp. 135-136
Keyword(s):  
Optimal Control ◽  
The Netherlands ◽  
Parallel Algorithms ◽  
Linear Systems ◽  
Large Scale

PRECISION SENSORS, ACTUATORS AND SYSTEMS. Edited by H S Tzou and T Fukuda, Kluwer Academic Publishers, Dordrecht, The Netherlands: 1992, pp 480, £105 (ISBN 0 79232 015 8) PARALLEL ALGORITHMS FOR OPTIMAL CONTROL OF LARGE SCALE LINEAR SYSTEMS. Zoran Gajic and Xuemin Shen, Springer-Verlag, Heidelberg: 1993, pp 455, DM 114 (ISBN 3 54019 825 3)

scholarly journals Parallel Algorithms for Solving Linear Systems on Hybrid Computers

2020 ◽  
pp. 53-66
Author(s):  
Alexander Khimich ◽  
Victor Polyanko ◽  
Tamara Chistyakova
Keyword(s):  
Parallel Algorithms ◽  
Computer Architecture ◽  
Linear Systems ◽  
High Performance ◽  
Numerical Data ◽  
Algebraic Equations ◽  
Existing Problems ◽  
Mathematical Properties ◽  
Linear Algebraic Equations ◽  
Computer Problem

Introduction. At present, in science and technology, new computational problems constantly arise with large volumes of data, the solution of which requires the use of powerful supercomputers. Most of these problems come down to solving systems of linear algebraic equations (SLAE). The main problem of solving problems on a computer is to obtain reliable solutions with minimal computing resources. However, the problem that is solved on a computer always contains approximate data regarding the original task (due to errors in the initial data, errors when entering numerical data into the computer, etc.). Thus, the mathematical properties of a computer problem can differ significantly from the properties of the original problem. It is necessary to solve problems taking into account approximate data and analyze computer results. Despite the significant results of research in the field of linear algebra, work in the direction of overcoming the existing problems of computer solving problems with approximate data is further aggravated by the use of contemporary supercomputers, do not lose their significance and require further development. Today, the most high-performance supercomputers are parallel ones with graphic processors. The architectural and technological features of these computers make it possible to significantly increase the efficiency of solving problems of large volumes at relatively low energy costs. The purpose of the article is to develop new parallel algorithms for solving systems of linear algebraic equations with approximate data on supercomputers with graphic processors that implement the automatic adjustment of the algorithms to the effective computer architecture and the mathematical properties of the problem, identified in the computer, as well with estimates of the reliability of the results. Results. A methodology for creating parallel algorithms for supercomputers with graphic processors that implement the study of the mathematical properties of linear systems with approximate data and the algorithms with the analysis of the reliability of the results are described. The results of computational experiments on the SKIT-4 supercomputer are presented. Conclusions. Parallel algorithms have been created for investigating and solving linear systems with approximate data on supercomputers with graphic processors. Numerical experiments with the new algorithms showed a significant acceleration of calculations with a guarantee of the reliability of the results. Keywords: systems of linear algebraic equations, hybrid algorithm, approximate data, reliability of the results, GPU computers.

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