Skip to main content
SpringerLink
Log in

An efficient and scalable block parallel algorithm of Neville elimination as a tool for the CMB maps problem

Journal of Mathematical Chemistry Aims and scope Submit manuscript

Cite this article

Abstract

This paper analyses the performance of several versions of a block parallel algorithm in order to apply Neville elimination in a distributed memory parallel computer. Neville elimination is a procedure to transform a square matrix A into an upper triangular one. This analysis must take into account the algorithm behaviour as far as execution time, efficiency and scalability are concerned. Special attention has been paid to the study of the scalability of the algorithms trying to establish the relationship existing between the size of the block and the performance obtained in this metric. It is important to emphasize the high efficiency achieved in the studied cases and that the experimental results confirm the theoretical approximation. Therefore, we have obtained a high predicting ability tool of analysis. Finally, we will present the elimination of Neville as an efficient tool in detecting point sources in cosmic microwave background maps.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Alonso P., Cortina R., Díaz I., Ranilla J.: Analyzing scalability of Neville elimination. J. Math. Chem. 40(1), 49 (2006)

    Article  CAS  Google Scholar 

  2. Alonso P., Cortina R., Díaz I., Ranilla J.: Scalability of Neville elimination using checkerboard partitioning. Int. J. Comput. Math. 85(3–4), 309 (2008)

    Article  Google Scholar 

  3. Alonso P., Cortina R., Díaz I., Ranilla J.: Blocking Neville elimination algorithm for exploiting cache memories. Appl. Math. Comput. 209, 2 (2009)

    Article  Google Scholar 

  4. Ando T.: Totally positive matrices. Linear Algebra Appl. 90, 165 (1987)

    Article  Google Scholar 

  5. Gasca M., Michelli C.A.: Total Positivity and its Applications. Kluwer, Dordrecht (1996)

    Google Scholar 

  6. Gasca M., Peña J.M.: Total positivity and Neville elimination. Linear Algebra Appl. 165, 25 (1992)

    Article  Google Scholar 

  7. Gemignani L.: Neville elimination for rank-structured matrices. Linear Algebra Appl. 428(4), 978 (2008)

    Article  Google Scholar 

  8. Grama A., Gupta A., Karypis G., Kumar V.: Introduction to Parallel Computing. Pearson Education Limited, London (2003)

    Google Scholar 

  9. Lin H., Bao H., Wang G.: Totally positive bases and progressive iteration approximation. Comput. Math. Appl. 50, 575 (2005)

    Article  Google Scholar 

  10. Lopez-Caniego M. et al.: Comparison of filters for the detection of point sources in Planck simulations. Mon. Not. Roy. Astron. Soc. 370, 2047 (2006)

    Article  Google Scholar 

  11. Peña J.M.: Shape Preserving Representations in Computer Aided–Geometric Design. Nova Science Publishers, New York (1999)

    Google Scholar 

  12. Penzias A.A., Wilson R.W.: A measurement of excess antenna temperature at 4080 Mc/s. Astrophys. J. 142, 419 (1965)

    Article  Google Scholar 

  13. Prieto M., Montero R.S., Llorente I.M., Tirado F.: A parallel multigrid solver for viscous flows on anisotropic structured grids. Parallel Comput. 29, 907 (2003)

    Article  Google Scholar 

  14. Smoot G. et al.: Structure in the COBE differential microwave radiometer first-year maps. Astrophys. J. 396, L1 (1992)

    Article  Google Scholar 

  15. Spergel D.N. et al.: First-year Wilkinson microwave anisotropy probe (WMAP) observations: determination of cosmological parameters. Astrophys. J. Suppl. 148, 175 (2003)

    Article  Google Scholar 

  16. J.A. Tauber, The Planck mission, in New Cosmological Data and the Values of the Fundamental Parameters. Proceedings of IAU Symposium vol. 201 (2005), p. 86, eds. by A. Lasenby, A. Wilkinson

  17. Toffolatti L. et al.: Extragalactic source counts and contributions to the anisotropies of the cosmic microwave background: predictions for the Planck Surveyor mission. Mon. Not. Roy. Astron. Soc. 297, 117 (1998)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Oviedo, 33203, Gijón, Spain

    P. Alonso

  2. Department of Computer Science, University of Oviedo, 33203, Gijón, Spain

    R. Cortina & J. Ranilla

  3. Department of Information System and Computation, Universidad Politécnica de Valencia, 46022, Valencia, Spain

    A. M. Vidal

Authors
  1. P. Alonso
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Cortina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Ranilla
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. A. M. Vidal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. Alonso.

Additional information

This is one of several papers published in Journal of Mathematical Chemistry, Special Issue: CMMSE 2010, with invited editorial contribution by Prof. Jesus Vigo-Aguiar.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Alonso, P., Cortina, R., Ranilla, J. et al. An efficient and scalable block parallel algorithm of Neville elimination as a tool for the CMB maps problem. J Math Chem 50, 345–358 (2012). https://doi.org/10.1007/s10910-010-9769-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-010-9769-0

Keywords

search

Navigation