COMPUTATION OF MONODROMY MATRIX ON FLOATING POINT ARITHMETIC WITH GODUNOV MODEL
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.
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- [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] Ö. Akın, H. Bulgak, Linear Difference Equations and Stability Theory, Sel¸cuk University
Research Centre of Applied Mathematics, No.2, Konya, 1998 (Turkish).
- [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] S.N. Elaydi, An Introduction to Difference Equations, Springer- Verlag, New York, 1996.
- [5] J. Rohn, Positive definiteness and stability of interval matrices, SIAM J. Matrix Anal. Appl.,
15(1) (1994) 175-184.
- [6] M. Voicu, O. Pastravanu, Generalized matrix diagonal stability and linear dynamical systems,
Linear Algebra Appl. 419 (2006) 299-310.
- [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] S.K. Godunov, The solution of systems of linear equations, Nauka, Moscow, 1980 (in Russian).
- [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] G. Bohlender, Floating-point computation of functions with maximum accuracy, IEEE Trans.
Comput., C-26 (7) (1977) 621-632.
- [11] U.W. Kulisch, Mathematical foundation of computer arithmetic, IEEE Trans. Comput., C-
26(7) (1977) 610-621.
- [12] U.W. Kulisch, W.L. Miranker, Computer Arithmetic in Theory and Practice, Academic Press
Inc., 1981.
- [13] U.W. Kulisch, Rounding Near Zero, Electrotechnical Laboratory, Agency of Industrial Science
and Technology, MITI, Tsukuba, Japan, 1999.
- [14] S.K. Godunov, Modern aspects of linear algebra, Translations of Mathematical Monographs, 175, Providence, RI : American Mathematical Society, 1998.
- [15] R.P. Agarwal, Difference Equations and Inequalities, 2nd ed., Pure and Applied Mathematics
Series, Vol. 228, National University of Singapore, 2000.
- [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] 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] H. Bulgak, D. Eminov, Computer dialogue system MVC, Sel¸cuk J. Appl. Math. 2(2) (2001)
17-38.