Journal ArticleDOI
Finding the roots of a polynomial on an MIMD multicomputer
Michel Consnard,Pierre Fraigniaud +1 more
- Vol. 15, pp 75-85
TLDR
It is shown that among the different classical processors networks topologies (ring, 2d-torus or n-cube), the hypercube topology minimizes the communications.Abstract:
This paper introduces the parallelization on a distributed memory multicomputer of two iterative methods for finding all the roots of a given polynomial. The parallel algorithms share the computation of the roots among the processors and perform a total exchange of the data at each step. Since the amount of communications is the main drawback of this approach, we study the effect of the network topology on the performance of the algorithms. Particularly, we show that among the different classical processors networks topologies (ring, 2d-torus or n-cube), the hypercube topology minimizes the communications. For each topology is computed the optimal number of processors. Experiments on the hypercube FPS T40 illustrate the results.read more
Citations
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Journal ArticleDOI
Methods and problems of communication in usual networks
TL;DR: A survey of existing methods of communication in usual networks, particularly the complete network, the ring, the torus, the grid, the hypercube, the cube connected cycles, the undirected de Bruijn graph, the stargraph, the shuffle-exchange graph, and the butterfly graph.
Journal ArticleDOI
Minimum linear gossip graphs and maximal linear (Δ, k)-gossip graphs †
TL;DR: This paper proves that the structure of minimum linear gossip graphs is independent of the relative values of the start‐up and unit propagation times, and shows that not all minimum broadcast graphs are maximal linear (Δ, k)‐gossip graphs.
Book ChapterDOI
Laguerre-like Methods for the Simultaneous Approximation of Polynomial Zeros
TL;DR: This paper considers some iterative methods of higher order for the simultaneous determination of polynomial zeros based on Euler’s third order method and proves that the presented methods have the order of convergence equal to four or more.
Journal ArticleDOI
Asymptotically optimal broadcasting and gossiping in faulty hypercube multicomputers
TL;DR: Various algorithms for reliable broadcasting and gossiping in faulty n-dimensional hypercube multicomputers are described and analyzed, and asymptotically optimal solutions for very short messages are proposed.
Journal ArticleDOI
Polynomial interpolation and polynomial root finding on OTIS-mesh
TL;DR: The optimality/near optimality of the algorithms is shown to achieve with the assumption that the data elements are initially stored following the row-column mapping and group mapping of theOTIS-mesh network.
References
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Journal ArticleDOI
Topological properties of hypercubes
Y. Saad,M.H. Schultz +1 more
TL;DR: The authors examine the hypercube from the graph-theory point of view and consider those features that make its connectivity so appealing and propose a theoretical characterization of the n-cube as a graph.
Journal ArticleDOI
Optimum broadcasting and personalized communication in hypercubes
S.L. Johnsson,C.-T. Ho +1 more
TL;DR: In this article, the authors proposed three spanning trees for the Boolean n-cube for the routing, and scheduling disciplines provably optimum within a small constant factor are proposed with appropriate scheduling and concurrent communication on all ports of every processor.
Journal ArticleDOI
On the efficiency of algorithms of analysis
TL;DR: In this paper, the authors present a novel approach to solve the problem of homonymity in homonym-based homonym identification: "homonymity" and "homophily".
Journal ArticleDOI
Iteration methods for finding all zeros of a polynomial simultaneously
TL;DR: Durand and Kerner as mentioned in this paper proposed a new derivation of their iteration equation, and a second, cubically convergent iteration method was proposed, with a relatively simple procedure for choosing the initial approximation.