Journal Article10.1016/0167-8191(93)90005-6
Parallel cyclic odd-even reduction algorithms for solving Toeplitz tridiagonal equations on MIMD computers
Michael P. Bekakos,David J. Evans +1 more
- 01 May 1993
- Vol. 19, Iss: 5, pp 545-561
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TL;DR: A thorough performance exposure and exploitation of a MIMD computer complex is carried out by presenting a selection of algorithms which implement a certain parallel evaluation routing and search for the optimal values of the granularity factor in accordance with some sequential subroutines permitted in the solution phase.
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Abstract: A thorough performance exposure and exploitation of a MIMD computer complex is carried out by presenting a selection of algorithms which implement a certain parallel evaluation routing and search for the optimal values of the granularity factor in accordance with some sequential subroutines permitted in the solution phase for most of the available parallel constructs of the machine in hand. For the cyclic odd-even reduction technique the symmetric constant-diagonal periodic case is chosen as the experimental vehicle, since it is more complicated and its concept indirectly includes that of the corresponding non-periodic case.
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Citations
A highly scalable parallel algorithm for solving Toeplitz tridiagonal systems of linear equations
TL;DR: A modification of the "Dichotomy Algorithm" (Terekhov, 2010) is proposed, aimed at parallel realization of a broad class of numerical methods including the inversion of Toeplitz and quasi-Toeplitzer tridiagonal matrices.
Efficiently solving tri-diagonal system by chunked cyclic reduction and single-GPU shared memory
Di Zhao,Jinhang Yu +1 more
TL;DR: This paper develops completely GPU shared memory-based chunked cyclic reduction under the constraint of the capacity of the shared memory, where solubility means the solvable tri-diagonal system with the maximum size of the coefficient matrix by the solver.
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•Dissertation
Design and evaluation of tridiagonal solvers for vector and parallel computers
Larriba Pey,Josep Lluís +1 more
- 10 Mar 1995
TL;DR: In this paper, the authors discuss the resolution of SISTEMAS TRIDIAGONALES DE ECUACIONES in the context of a new metoda.
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TL;DR: With the actual physical size of components being very small and the high circuit density, there is little scope for improving computation speech significantly by such means as even denser circuitry or still faster electronic components.
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A study of algorithms for parallel computers and VLSI systolic processor arrays
Michael P. Bekakos
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TL;DR: LisT Qp fiGURES LisT OF TABLES as mentioned in this paper ) is a collection of tables from the Web: http://www.web-blogs.com/webblogs.
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The Numerical Solution of Non-Linear Parabolic Equations on MIMD Parallel Computers
M. P. Bekakos,D. J. Evans +1 more
- 01 Jan 1986
TL;DR: This paper investigates the applicability of a new class of group explicit methods to parallel processing, the experimental vehicle being a non-linear parabolic p.d.e. of second order.
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