Abstract
Solving the matrix inversion is an open problem which is often related to scientific computation. Moreover, matrix inverse also has wide applications in social networks. Individuals in social networks are described as nodes, and the similarity among nodes are significant for link prediction. Usually, the problem of calculating similarities among nodes is converted to the problem of matrix inversion. With the increasing of the orders of matrices, traditional sequential algorithms are unable to meet the needs for the short calculation time. Although cluster systems can solve the inversion of large-scale matrices efficiently, the equipment cost and power consumption are very high. This paper proposes a parallel algorithm PA-Gauss, which is based on the Gauss-Jordan method of selecting the main element. CUDA (Computer Unified Device Architecture) of GPU (Graphic Process Unit) is used to implement the proposed algorithm to solve inversions of the real and complex matrices. The experimental results show that the Gauss-Jordan algorithm can save more running time than traditional sequential algorithms and the speedup ratio of PA-Gauss for Real Matrices is 633~100435, and the speedup ratio of PA-Gauss for Complex Matrices is 224~36508. Therefore,the computing time of solving the matrix inversions is reduced significantly.
This work is supported by Program for Group of Science and Technology Innovation of Heilongjiang Educational Committee under grant No.2013TD012, the Science and Technology Research of Heilongjiang Educational Committee under grant No.12511395.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Nash, J.C.: Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, 2nd edn. Adam Hilger, Bristol (1990)
Brini, A., Marino, M., Stevan, S.: The uses of the refined matrix model recursion. Journal of Mathematical Physics 52(5), 291–315 (2011)
Chakrabarti, S.: Dynamic personalized pagerank in entity-relation graphs. In: 16th International Conference on World Wide Web (WWW), pp. 571–580. ACM, New York (2007)
Tong, H., Faloutsos, C., Koren, Y.: Fast direction-aware proximity for graph mining. In: 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD), pp. 747–756. ACM, New York (2007)
Foo, S.L., Silvester, P.P.: Finite Element Analysis of Inductive Strips in Unilateral Finlines. IEEE Microwave Theory and Techniques 41(2), 298–304 (1993)
Jodr, L., Law, A.G., Rezazadeh, A., Watson, J.H., Wu, G.: Computations for the Moore-Penrose and Other Generalized Inverses. Congress. Numer. 80, 57–64 (1991)
Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (1992)
Aqrawi, A.A.: Three Dimensional Convolution of Large Data Sets on Modern GPUs. Norwegian University of Science and Technology (2009)
Barnat, J., Bauch, P., Brim, L., Ceska, M.: Computing Strongly Connected Components in Parallel on CUDA. In: 25th IEEE International Symposium on Parallel and Distributed Processing (IPDPS), pp. 544–555. IEEE Press, New York (2011)
Hagiescu, A., Huynh, H.P., Wong, W., Goh, R.S.M.: Automated architecture-aware mapping of streaming applications onto GPUs. In: 25th IEEE International Symposium on Parallel and Distributed Processing (IPDPS), pp. 467–478. IEEE Press, New York (2011)
Ben-Israel, A., Greville, T.N.E.: Generalized Inverses:Theory and Applications. Wiley-Interscience, New York (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Tian, N., Guo, L., Ren, M., Ai, C. (2014). Implementing the Matrix Inversion by Gauss-Jordan Method with CUDA. In: Cai, Z., Wang, C., Cheng, S., Wang, H., Gao, H. (eds) Wireless Algorithms, Systems, and Applications. WASA 2014. Lecture Notes in Computer Science, vol 8491. Springer, Cham. https://doi.org/10.1007/978-3-319-07782-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-07782-6_5
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07781-9
Online ISBN: 978-3-319-07782-6
eBook Packages: Computer ScienceComputer Science (R0)