A class of interconnection networks based on some existing permutation networks is described with applications to processor to memory communication in multiprocessing systems. These networks, termed delta networks, allow a direct link between any processor to any memory module. The delta networks and full crossbars are analyzed with respect to their effective bandwidth and cost. The analysis shows that delta networks have a far better performance per cost than crossbars in large multiprocessing systems.

Performance of Processor-Memory Interconnections for Multiprocessors

Kurskod: 5DV050 Inrättad: 2008-03-31 Inrättad av: teknisk-naturvetenskapliga fakultetsnämnden Reviderad: 2012-02-29 Reviderad av: teknisk-naturvetenskapliga fakultetsnämnden Kursplan giltig från: 2012, vecka 10 Ansvarig enhet: Inst för datavetenskap SCB-ämnesrubrik: Informatik/Dataoch systemvetenskap Huvudområden och successiv fördjupning: Beräkningsteknik: Avancerad nivå, har endast kurs/er på grundnivå som förkunskapskrav (A1N) , Datavetenskap: Avancerad nivå, har endast kurs/er på grundnivå som förkunskapskrav (A1N) Betygsskala: För denna kurs ges betygen 5 Med beröm godkänd, 4 Icke utan beröm godkänd, 3 Godkänd, VG Väl godkänd, G Godkänd, U Underkänd Utbildningsnivå: Avancerad nivå

The design and analysis of parallel algorithms

The authors' survey paper is devoted to the present state of computational methods in linear algebra. Questions discussed are the means and methods of estimating the quality of numerical solution of computational problems, the generalized inverse of a matrix, the solution of systems with rectangular and poorly conditioned matrices, the inverse eigenvalue problem, and more traditional questions such as algebraic eigenvalue problems and the solution of systems with a square matrix (by direct and iterative methods).

Computational methods of linear algebra

J. A. George has discovered a method, called nested dissection, for solving a system of linear equations defined on an n = k $\times$ k square grid in O(n log n) space and O($n{3/2}$) time. We generalize this method without degrading the time and space bounds so that it applies to any system of equations defined on a planar or almost-planar graph. Such systems arise in the solution of two-dimensional finite element problems. Our method uses the fact that planar graphs have good separators. More generally, we show that sparse Gaussian elimination is efficient for any class of graphs which have good separators, and conversely that graphs without good separators (including almost all sparse graphs) are not amenable to sparse Gaussian elimination.

Generalized nested dissection

Publisher Summary This chapter discusses algebraic complexity theory. Complexity theory, as a project of lower bounds and optimality, unites two quite different traditions. The first comes from mathematical logic and the theory of recursive functions. In this, the basic computational model is the Turing machine. The second tradition has developed from questions of numerical algebra. The problems in this typically have a fixed finite size. Consequently, the computational model is based on something like an ordinary computer that however is supplied with the ability to perform any arithmetic operation with infinite precision and that in turn is required to deliver exact results. The formal model is that of straight-line program or arithmetic circuit or computation sequence, more generally that of computation tree.

Algebraic Complexity Theory.

The fast matrix multiplication algorithm by Strassen is used to obtain the triangular factorization of a permutation of any nonsingular matrix of order n in 2.35, i.e. if n > (2.35)5 t 100. Strassen uses block LDU factorization (Householder (2, p. 126)) recursively to compute the inverse of a matrix of order m2k by m2k divisions, < (6/5)m37k - m2k multiplications, and < (6/5)(5 + m)m27k - 7(m2k)2 additions. The inverse of a matrix of order n could then be computed by ? (5.64)nlO02 7 arithmetic operations.

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James R. Bunch

Papers

Triangular Factorization and Inversion by Fast Matrix Multiplication