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New variants of the quadrant interlocking factorisation (Q.I.F.) method

  • Parallelism Of Numerical Algorithms
  • Conference paper
  • First Online:
Conpar 81 (CONPAR 1981)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 111))

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Abstract

New factorisation methods suitable for the solution of linear equations applicable to parallel computers are proposed in this paper. The methods are based on variations to the Quadrant Interlocking Factorisation (Q.I.F.) methods given earlier in Evans and Hadjidimos [1] and Evans and Hatzopoulos [2]. The new methods can be considered as the Crout and Gauss-Jordan type for general real matrices and Choleski type for matrices which are positive definite. The paper also includes topics such as error analysis and computational cost analysis for the proposed methods.

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References

  1. Evans, D.J., and Hadjidimos A., "The Parallel Solution of Linear System", International Journal of Computer Mathematics, Vol.8, pp.149–166 (1980).

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  2. Evans, D.J., and Hatzopoulos, M., "Modification to the Quadrant Interlocking Factorisation Parallel Method", International Journal of Computer Mathematics, Vol.7, pp.227–238 (1979).

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  3. Flynn, M.J., "Some Computer Organisations and Their Effectiveness", IEEE Trans. on Computers C-21, pp.948–960 (1972).

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  4. Stone, H.S., "Problems of Parallel Computation" in ‘Complexity of Sequential and Parallel Numerical Algorithms', (Edit. J.F. Traub), 1–16, Academic Press, (1973).

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  5. Kuck, D.J., Multi-operation Machine Computational" in ‘Complexity of Sequential and Parallel Numerical Algorithms', see [4].

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  6. Martin, R.S., Reinsch C. and Wilkinson, J.H., "Householder's Tridiagonalisation of a Symmetric Matrix", Nat.Bur. of Standards, A.M.S., No.57, pp.22–24, (1960).

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  7. Shanehchi, J., "The Determination of Sparse Eigensystems and Parallel Linear System Solvers", Ph.D. Thesis, Loughborough University of Technology, (1980).

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  8. Wilkinson, J.H., "Rounding Errors in Algebraic Processes", H.M.S.O., (1963).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Studies, Loughborough University of Technology, Loughborough, Leicestershire, UK

    J. Shanehchi & D. J. Evans

Authors
  1. J. Shanehchi
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  2. D. J. Evans
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Editor information

W. Brauer P. Brinch Hansen D. Gries C. Moler G. Seegmüller J. Stoer N. Wirth Wolfgang Händler

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© 1981 Springer-Verlag Berlin Heidelberg

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Shanehchi, J., Evans, D.J. (1981). New variants of the quadrant interlocking factorisation (Q.I.F.) method. In: Brauer, W., et al. Conpar 81. CONPAR 1981. Lecture Notes in Computer Science, vol 111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105140

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  • DOI: https://doi.org/10.1007/BFb0105140

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10827-6

  • Online ISBN: 978-3-540-38715-2

  • eBook Packages: Springer Book Archive

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