Skip to main content
SpringerLink
Log in
Book cover

International Conference on Smart Cities, Infrastructure, Technologies and Applications

SCITA 2017: Smart Societies, Infrastructure, Technologies and Applications pp 296–305Cite as

Performance Evaluation of Jacobi Iterative Solution for Sparse Linear Equation System on Multicore and Manycore Architectures

  • Conference paper
  • First Online:

Abstract

One of the common and pressing challenges in solving real-world problems in various domains, such as in smart cities, involves solving large sparse systems of linear equations. Jacobi iterative method is used to solve such systems in case if they are diagonally dominant. This research focuses on the parallel implementation of the Jacobi method to solve large systems of diagonally dominant linear equations on conventional CPUs and Intel Xeon Phi co-processor. The performance is reported on the two architectures with a comparison in terms of the execution times.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Altowaijri, S., Mehmood, R., Williams, J.: A quantitative model of grid systems performance in healthcare organisations. In: 2010 International Conference on Intelligent Systems, Modelling and Simulation, pp. 431–436. IEEE (2010)

    Google Scholar 

  2. Mehmood, R., Lu, J.A.: Computational Markovian analysis of large systems. J. Manuf. Technol. Manag. 22, 804–817 (2011)

    Article  Google Scholar 

  3. Mehmood, R., Alturki, R., Zeadally, S.: Multimedia applications over metropolitan area networks (MANs). J. Netw. Comput. Appl. 34, 1518–1529 (2011)

    Article  Google Scholar 

  4. Mehmood, R., Meriton, R., Graham, G., Hennelly, P., Kumar, M.: Exploring the influence of big data on city transport operations: a Markovian approach. Int. J. Oper. Prod. Manag. 37, 75–104 (2017)

    Article  Google Scholar 

  5. Mehmood, R., Graham, G.: Big data logistics: a health-care transport capacity sharing model. Procedia Comput. Sci. 64, 1107–1114 (2015)

    Article  Google Scholar 

  6. Liu, W., Vinter, B.: CSR5: An Efficient Storage Format for Cross-Platform Sparse Matrix-Vector Multiplication (2015)

    Google Scholar 

  7. Pissanetzky, S.: Sparse Matrix Technology electronic edition

    Google Scholar 

  8. Saad, Y.: Iterative Methods for Sparse Linear Systems. Society for Industrial and Applied Mathematics, Philadelphia (2003)

    Book  Google Scholar 

  9. Mehmood, R.: Serial disk-based analysis of large stochastic models. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 230–255. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24611-4_7

    Chapter  MATH  Google Scholar 

  10. Mehmood, R., Crowcroft, J.: Parallel iterative solution method for large sparse linear equation systems. Technical report Number UCAM-CL-TR-650, Computer Laboratory, University of Cambridge, Cambridge, UK (2005)

    Google Scholar 

  11. Goumas, G., Kourtis, K., Anastopoulos, N., Karakasis, V., Koziris, N.: Performance evaluation of the sparse matrix-vector multiplication on modern architectures. J. Supercomput. 50, 36–77 (2009)

    Article  Google Scholar 

  12. Im, E.-J., Yelick, K., Vuduc, R.: Sparsity: optimization framework for sparse matrix kernels. Int. J. High Perform. Comput. Appl. 18, 135–158 (2004)

    Article  Google Scholar 

  13. Vuduc, R.W.: Automatic performance tuning of sparse matrix kernels (2003). https://dl.acm.org/citation.cfm?id=1023242

  14. Williams, S., Oliker, L., Vuduc, R., Shalf, J., Yelick, K., Demmel, J.: Optimization of sparse matrix-vector multiplication on emerging multicore platforms. Parallel Comput. 35, 178–194 (2009)

    Article  Google Scholar 

  15. Mellor-Crummey, J., Garvin, J.: Optimizing sparse matrix-vector product computations using unroll and jam. Int. J. High Perform. Comput. Appl. 18, 225–236 (2004)

    Article  Google Scholar 

  16. Pinar, A., Heath, M.T.: Improving performance of sparse matrix-vector multiplication. In: Proceedings of the 1999 ACM/IEEE conference on Supercomputing (CDROM) - Supercomputing 1999, p. 30–es. ACM Press, New York (1999)

    Google Scholar 

  17. Nishtala, R., Vuduc, R., Demmel, J.W., Yelick, K.A.: When cache blocking of sparse matrix vector multiply works and why. Appl. Algebra Eng. Commun. Comput. 18, 297–311 (2007)

    Article  MathSciNet  Google Scholar 

  18. Vuduc, R.W., Moon, H.-J.: Fast sparse matrix-vector multiplication by exploiting variable block structure. In: Yang, L.T., Rana, O.F., Di Martino, B., Dongarra, J. (eds.) HPCC 2005. LNCS, vol. 3726, pp. 807–816. Springer, Heidelberg (2005). https://doi.org/10.1007/11557654_91

    Chapter  Google Scholar 

  19. Deshmukh, O., Negrut, D.: Characterization of Intel Xeon Phi for linear algebra workloads (2014)

    Google Scholar 

  20. Liu, X., Smelyanskiy, M., Chow, E., Dubey, P.: Efficient sparse matrix-vector multiplication on x86-based many-core processors. In: Proceedings of the 27th international ACM conference on International conference on supercomputing - ICS 2013, p. 273. ACM Press, New York (2013)

    Google Scholar 

  21. Kreutzer, M., Hager, G., Wellein, G., Fehske, H., Bishop, A.R.: A unified sparse matrix data format for efficient general sparse matrix-vector multiplication on modern processors with wide simd units. SIAM J. Sci. Comput. 36, C401–C423 (2014)

    Article  MathSciNet  Google Scholar 

  22. Bylina, B., Potiopa, J.: Explicit fourth-order Runge-Kutta method on Intel Xeon Phi coprocessor. Int. J. Parallel Program. 45, 1073–1090 (2017)

    Article  Google Scholar 

  23. Bylina, B., Potiopa, J.: Data structures for Markov chain transition matrices on Intel Xeon Phi. In: 2016 Federated Conference on Computer Science and Information Systems (2016)

    Google Scholar 

  24. Saule, E., Kaya, K., Çatalyürek, Ü.V.: Performance evaluation of sparse matrix multiplication kernels on Intel Xeon Phi. Presented at the 2014 (2014)

    Google Scholar 

Download references

Acknowledgements

The experiments reported in this paper were performed on the Aziz supercomputer at King Abdul Aziz University, Jeddah, Saudi Arabia.

Author information

Authors and Affiliations

  1. Faulty of Information Technology, King Abdul Aziz University, Jeddah, Saudi Arabia

    Samiah Alzahrani & Iyad Katib

  2. Fujitsu Technology Solutions, Jeddah, Saudi Arabia

    Mohammad Rafi Ikbal & Mahmoud Fayez

  3. High Performance Computing Center, King Abdulaziz University, Jeddah, Saudi Arabia

    Rashid Mehmood

Authors
  1. Samiah Alzahrani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Rafi Ikbal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rashid Mehmood
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mahmoud Fayez
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Iyad Katib
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Rafi Ikbal .

Editor information

Editors and Affiliations

  1. King Abdulaziz University, Jeddah, Saudi Arabia

    Rashid Mehmood

  2. Geographic Information Science and Technology, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA

    Budhendra Bhaduri

  3. King Abdulaziz University, Jeddah, Saudi Arabia

    Iyad Katib

  4. European Alliance for Innovation, Bratislava, Slovakia

    Imrich Chlamtac

Rights and permissions

Reprints and permissions

Copyright information

© 2018 ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Alzahrani, S., Ikbal, M.R., Mehmood, R., Fayez, M., Katib, I. (2018). Performance Evaluation of Jacobi Iterative Solution for Sparse Linear Equation System on Multicore and Manycore Architectures. In: Mehmood, R., Bhaduri, B., Katib, I., Chlamtac, I. (eds) Smart Societies, Infrastructure, Technologies and Applications. SCITA 2017. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 224. Springer, Cham. https://doi.org/10.1007/978-3-319-94180-6_28

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-94180-6_28

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94179-0

  • Online ISBN: 978-3-319-94180-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation