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

  • J. Shanehchi
  • D. J. Evans
Parallelism Of Numerical Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 111)

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.

Keywords

Linear System Coefficient Matrix Factorisation Method Root Operation Hand Side Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Evans, D.J., and Hadjidimos A., "The Parallel Solution of Linear System", International Journal of Computer Mathematics, Vol.8, pp.149–166 (1980).zbMATHMathSciNetGoogle Scholar
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    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).zbMATHMathSciNetGoogle Scholar
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    Kuck, D.J., Multi-operation Machine Computational" in ‘Complexity of Sequential and Parallel Numerical Algorithms', see [4].Google Scholar
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    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).Google Scholar
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    Shanehchi, J., "The Determination of Sparse Eigensystems and Parallel Linear System Solvers", Ph.D. Thesis, Loughborough University of Technology, (1980).Google Scholar
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    Wilkinson, J.H., "Rounding Errors in Algebraic Processes", H.M.S.O., (1963).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • J. Shanehchi
    • 1
  • D. J. Evans
    • 1
  1. 1.Department of Computer StudiesLoughborough University of TechnologyLoughboroughUK

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