Convergence of The Barzilai-Borwein Method for Solving Slightly Unsymmetric Linear Systems

Authors

  • Bayda G. Fathi University of Zakho

Keywords:

Unsymmetric linear algebraic equations, Barzilai and Borwein gradient method, symmetric and skew-symmetric matrices, eigenvalues, condition number

Abstract

Due to its simplicity and numerical efficiency, the Barzilai and Borwein (BB) gradient method has received numerous attentions in different scientific fields. In this paper, the sufficient condition for convergence of the BB method when the coefficient matrix of linear algebraic equations is slightly unsymmetric with positive definite symmetric part is presented

Author Biography

Bayda G. Fathi, University of Zakho

Dept. of Mathematics, Faculty of Science, University of Zakho, Kurdistan Region-Iraq

References

Barzilai, J. and Borwein, J. M.: Two-point step size gradient methods. IMA Journal of Numerical Analysis, 8, pp. 141–148, 1988.

Dai, Y. H. and Fletcher, R.: On the asymptotic behaviour of some new gradient methods. Mathematical Programming, 103(3), pp541–559, 2005.

Dai, Y. H. and Liao, L. Z.: R-linear convergence of the Barzilai and Borwein method for unconstrained optimization. IMA Journal of Numerical Analysis, 1, pp. 1–10, 2002.

Dennis, J. E. and Schnabel, R. B: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, NJ, 1983.

Fletcher, R.: Practical Methods of Optimization. Wiley, 2nd edition, 2000.

Raydan, M. M.: On the Barzilai and Borwein choice of steplength for the gradient method. IMA Journal of Numerical Analysis, 13, pp. 321–326, 1993.

Raydan, M. M.: Convergence propreties of the Barzilai and Borwein gradient method. PhD thesis, Rice University, 1991.

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Published

2015-06-30

How to Cite

Fathi, B. G. (2015). Convergence of The Barzilai-Borwein Method for Solving Slightly Unsymmetric Linear Systems. Science Journal of University of Zakho, 3(1), 140–144. Retrieved from https://sjuoz.uoz.edu.krd/index.php/sjuoz/article/view/118

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Section

Science Journal of University of Zakho