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Parallel algorithm on inversion for adjacent pentadiagonal matrices with MPI

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Abstract

In this work, the method based on the work of Huang and McColl on analytical inversion of general tridiagonal matrices is parallelized with MPI. The proposed method is not only capable of finding inverses of full pentadiagonal matrices, but also of those with pentadiagonal envelope, such as tridiagonal matrices. The method is modified to generate an MPI algorithm. The speed-up performance of the parallelized algorithm is also analyzed on different cases.

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References

  1. Benson A, Evans DJ (1977) A normalized algorithm for the solution of positive definite symmetric quindiagonal systems of linear equations. ACM Trans Math Softw 3(1):96–103

    Article  MATH  Google Scholar 

  2. Ivins J, Porrill J (1993) Everything you always wanted to know about snakes. AIVRU Technical Memo no 86

  3. Becker JC, Nitzberg B, Van der Wijngaart RF (1997) Predicting cost/performance trade-offs for Whitney: a commodity computing cluster. NAS technical report NAS-97-023

  4. Jin H, Frumkin M, Yan J (1999) The OpenMP implementations of NAS parallel benchmarks and its performance. NAS technical report NAS-99-011

  5. Zhao X, Huang T (2008) On the inverse of a general pentadiagonal matrix. Appl Math Comput 202:639–646

    Article  MATH  MathSciNet  Google Scholar 

  6. Hadj ADA, Elouafi M (2008) A fast numerical algorithm for the inverse of a tridiagonal and pentadiagonal matrix. Appl Math Comput 202:441–445

    Article  MATH  MathSciNet  Google Scholar 

  7. Kanal ME, Baykara NA, Demiralp M (2003) A novel approach to the numerical inversion algorithm for adjacent pentadiagonal matrices. In: Fourth international conference, tools for mathematical modelling, St Petersburg, Russia

  8. Huang GH, McColl WF (1997) Analytical inversion of general tridiagonal matrices. J Phys A, Math Gen 30:7919–7933

    Article  MATH  MathSciNet  Google Scholar 

  9. Barney B (2010) Lawrence Livermore: National laboratory tutorials: introduction to parallel computing, designing parallel programs. https://computing.llnl.gov/tutorials/parallel_comp/

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Authors and Affiliations

  1. Department of Computational Science and Engineering, Informatics Institute, İstanbul Technical University, 34469, İstanbul, Turkey

    M. E. Kanal

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  1. M. E. Kanal
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Correspondence to M. E. Kanal.

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Kanal, M.E. Parallel algorithm on inversion for adjacent pentadiagonal matrices with MPI. J Supercomput 59, 1071–1078 (2012). https://doi.org/10.1007/s11227-010-0487-y

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  • DOI: https://doi.org/10.1007/s11227-010-0487-y

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