This paper presents a criteria for the existence and uniqueness of solutions to first order fuzzy difference system using QR-algorithm. Modified QR-algorithm is presented for fuzzy linear systems using singular value decomposition.
References
R. Kannan, Minkowski's convex body theorem and integer programming
p 415-440(1987)
Murty, K. N., Andreou, S., Viswanadh, K. V. K., Qualitative properties of general first order matrix difference systems. Nonlinear Studies, 16(2009), no. 4, 359--370.
K.N. Murty, Yan Wu, Viswanadh V. Kanuri, Metrics that suit for dichotomy, well conditioning of object oriented design, Nonlinear Studies, Vol 18, No: 4, P: 621--637 (2013)
Kasi Viswanadh V Kanuri, Existence Of Ψ-Bounded Solutions For Fuzzy Dynamical Systems On Time Scales, International Journal of Scientific & Engineering Research, 2020, Vol. 11, No. 5, 613--624.
Kasi Viswanadh V. Kanuri, K. N. Murty, “Three-Point boundary value problems associated with first order matrix difference system-existence and uniqueness via shortest and closest Lattice vector methods”, Journal of Nonlinear Sciences and Applications, Volume 12, Issue 11, (2019) 720--727
K. N. Murty, V. V. S. S. S. Balaram, K.V. K. Viswanadh, “Solution of Kronecker Product Initial Value Problems Associated with First Order Difference System via Tensor-based Hardness of the Shortest Vector Problem”, Electronic Modeling, vol. 6, p: 19--33 (2008).
K.N. Murty, K.V.K. Viswanadh, P. Ramesh, Yan Wu, “Qualitative properties of a system of differential equation involving Kronecker product of matrices”, Nonlinear Studies, Vol 20, No: 3, P: 459--467 (2013)
Kasi Viswanadh V. Kanuri, R. Suryanarayana, K. N. Murty, Existence of Ψ-bounded solutions for linear differential systems on time scales, Journal of Mathematics and Computer Science, 20 (2020), no. 1, 1--13.
Rice, J.R. (1966), Experiments of Gram-Schmidt Orthogonalization, Math-Comp., Vol. 20, pp. 325-328
V. Lakshmikantham & Donato Trigiante ,Theory of Difference Equations : Numerical Methods and Applications ,Academic press, INC 1988
N. Swapna, S. Udaya Kumar ,Best Least Square Solution of Boundary Value Problems Associated with a System of First Order Matrix Differential Equation electronic Modelling Vol 38 pg1-14 (2015)
Charyulu L.N. Rompicharla , Sundaranand V.Putcha and G.V.S.R.Deekshitulu., Existence Of (Φ⊗Ψ) Bounded Solutions for Linear First Order Kronecker Product Systems, 2020, International Journal of Recent Scientific Research, 11(06), pp. 39047-39053
