IJAM: Volume 37, No. 5 (2024)

DOI: 10.12732/ijam.v37i5.3

 

COMPUTATIONAL METHOD FOR FIRST

THREE DOMINANT EIGENMODES

OF SYMMETRIC MATRICES

 

 

Pravin Singh 1, Virath Singh 2,§, Shivani Singh 3

 

 

1 University of KwaZulu-Natal

Private Bag X54001

Durban - 4001, SOUTH AFRICA

 

2 University of KwaZulu-Natal

Private Bag X54001

Durban - 4001, SOUTH AFRICA

 

3 University of South Africa

Department of Decision Sciences

P.O. Box 392, Pretoria - 0003, SOUTH AFRICA

 

Abstract.  In this paper we advocate a new method to compute the first three dominant eigenmodes of real symmetric matrices. Our method avoids deflation and can even compute the second and third mode, bypassing the need to compute the first mode.

 

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How to cite this paper?
DOI: 10.12732/ijam.v3
7i5.3
Source: 
International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 202
4
Volume: 3
7
Issue: 5

References

 

[1] T. D. Frank, Eigenvalue analysis of SARS-CoV-2 viral load data: Illustration for eight COVID-19 patients, Int. J. Data Sci. Anal. 15, No 3 (2023), 281–290;
doi:10.1007/s41060-022-00319-y.

[2] G. Gu, F. Xie, Ke Zhang, A two-step matrix splitting iteration for computing the PageRank, Journal of Computational and Applied Mathematics, 278 (2015), 19–28.

[3] D. A. Gregory, D. Hershkowitz, S. J. Kirkland, The spread of the spectrum of a graph, Linear Algebra and its Applications, 332–334 (2001), 23–35.

[4] H. Wolkowicz, G. P. H. Styan, Bounds for eigenvalues using traces, Linear Algebra and its Applications, 29 (1980), 471–506.

[5] R. Sharma, R. Kumar, R. Saini, Note on bounds for eigenvalues using traces, arXiv:1409.0096v1, Functional Analysis (2014).

[6] P. Singh, V. Singh, S. Singh, New bounds for the maximal eigenvalues of positive definite matrices, International Journal of Applied Mathematics, 35, No 5 (2022), 685–691; doi:10.12732/ijam.v35i5.4.

[7] P. Singh, S. Singh, V. Singh, Results on bounds of the spectrum of positive definite matrices by projections, Aust. J. Math. Anal. Appl., 20, No 2 (2023), Art. 3, 10 pp.

[8] D. K. Faddeev, V. N. Faddeeva, Computational Methods of Linear Algebra, WH Freeman and Company, San Francisco and London (1963).

[9] R. Horn, C. A. Johnson, Matrix Analysis, Cambridge University Press (2012), 345–346.

[10] K. V. Singh, Y. M. Ram, Numerical deflation of the transcendental eigenvalue problem, Mechanical Systems and Signal Processing, 83 (2017), 522–532.

[11] R. T. Gregory, D. L. Karney, A Collection of Matrices for Testing Computational

Algorithms, Robert E Krieger Publishing Company, New York (1978).

[12] B. Boehmke, B. M. Greenwell, Hands-On Machine Learning with R, Chapman and Hall (2019), 343–396; ISBN 978-1-138-49568-5.

[13] I. T. Jolliffe, J. Cadima, Principal component analysis: A review and recent developments, Philosophical Transactions of the Royal Society A, 374 (2016); doi:10.1098/rsta.20150202.

[14] B. Venkataseshaiah, K. N. Roopadevi, S. Michahial, Image compression using singular value decomposition, International Journal of Advanced Research in Computer and Communication Engineering, 5, No 12 (2016).

[15] M. Manathunga, H. M. Aktulga, A. W. Gotz, K. M. Merz, Quantum mechanics/ molecular mechanics simulations on NVIDIA and AMD Graphics processing units, Journal of Chemical Information and Modeling, 63, No 3 (2013), 711–717.

[16] M. Zareh, L. Sabattini, C. Secchi, Distributed Laplacian eigenvalue and eigenvector estimation in multi-robot systems, Distributed Autonomous Robotic Systems. Springer Proceedings in Advanced Robotics, 6, (2018), Springer Cham;
doi:10.1007/978-3-319-73008-0 14.

[17] M. Slavkovic, D. Jevtic, Face recognition using eigenface approach, Serbian Journal of Electrical Engineering, 9, No 1 (2012), 121–130.

[18] R. Drikvandi, O. Lawal, Sparse principal component analysis for natural language processing, Annals of Data Science, 10, No 1 (2023), 25–41; doi:10.1007/s40745-020-00277-x.

[19] C. D. Meyer, Matrix Analysis and Applied Linear Algebra, SIAM, Philadelphia (2000).

 

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