COMPUTATION OF MONODROMY MATRIX ON FLOATING POINT ARITHMETIC WITH GODUNOV MODEL

Abstract

The results computed monodromy matrix on floating point arithmetics according to Wilkinson Model have been given in [1]. In this study, new results have been obtained by examining floating point arithmetics with respect to Godunov Model the results in [1]. These results have been applied to Schur stability of system of linear difference equations with periodic coefficients. Also the effect of floating point arithmetics has been investigated on numerical examples.

Keywords

• Floating point,Godunov model,fundamental matrix,monodromy matrix,Schur stability,linear difference equations,periodic coefficients

References

1. [1] A.O. Çıbıkdiken, K. Aydın, Computation of the monodromy matrix in floating point arithmetic with the Wilkinson Model, Comput Math Appl, Volume 67, Issue 5, March 2014, Pages 1186-1194.
2. [2] Ö. Akın, H. Bulgak, Linear Difference Equations and Stability Theory, Sel¸cuk University Research Centre of Applied Mathematics, No.2, Konya, 1998 (Turkish).
3. [3] K. Aydın, The Condition Number for the Asymptotic Stability of the Periodic Ordinary Differential Systems, Ph.D. Thesis, Sel¸cuk University Graduate Natural and Applied Sciences, Konya, 1996 (Turkish).
4. [4] S.N. Elaydi, An Introduction to Difference Equations, Springer- Verlag, New York, 1996.
5. [5] J. Rohn, Positive definiteness and stability of interval matrices, SIAM J. Matrix Anal. Appl., 15(1) (1994) 175-184.
6. [6] M. Voicu, O. Pastravanu, Generalized matrix diagonal stability and linear dynamical systems, Linear Algebra Appl. 419 (2006) 299-310.
7. [7] K. Aydın, H. Bulgak, G.V. Demidenko, Numeric characteristics for asymptotic stability of solutions to linear difference equations with periodic coefficients, Sib. Math. J. 41(6) (2000) 1005-1014.
8. [8] S.K. Godunov, The solution of systems of linear equations, Nauka, Moscow, 1980 (in Russian).

9. [9] S.K. Godunov, A.G. Antonov, O.P. Kiriluk, V.I. Kostin, Guaranteed Accuracy in Mathematical Computations, Englewood Cliffs, N. J., Prentice- Hall, 1993.
10. [10] G. Bohlender, Floating-point computation of functions with maximum accuracy, IEEE Trans. Comput., C-26 (7) (1977) 621-632.
11. [11] U.W. Kulisch, Mathematical foundation of computer arithmetic, IEEE Trans. Comput., C- 26(7) (1977) 610-621.
12. [12] U.W. Kulisch, W.L. Miranker, Computer Arithmetic in Theory and Practice, Academic Press Inc., 1981.
13. [13] U.W. Kulisch, Rounding Near Zero, Electrotechnical Laboratory, Agency of Industrial Science and Technology, MITI, Tsukuba, Japan, 1999.
14. [14] S.K. Godunov, Modern aspects of linear algebra, Translations of Mathematical Monographs, 175, Providence, RI : American Mathematical Society, 1998.
15. [15] R.P. Agarwal, Difference Equations and Inequalities, 2nd ed., Pure and Applied Mathematics Series, Vol. 228, National University of Singapore, 2000.
16. [16] K. Aydın, H. Bulgak, G.V. Demidenko, Continuity of numeric characteristics for asymptotic stability of solutions to linear difference equations with periodic coefficients, Sel¸cuk J. of Appl. Math. 2(2) (2001) 5-10.
17. [17] K. Aydın, H. Bulgak, G.V. Demidenko, Asymptotic stability of solutions to perturbed linear difference equations with periodic coefficients, Sib. Math. J. 43(3) (2002) 389–401.
18. [18] H. Bulgak, D. Eminov, Computer dialogue system MVC, Sel¸cuk J. Appl. Math. 2(2) (2001) 17-38.