Conserved quantities of the discrete finite Toda equation and lower bounds of the minimal singular value of upper bidiagonal matrices

Subtraction-free recurrence relations for lower bounds of the minimal singular value of an upper bidiagonal matrix

On an N × N upper bidiagonal matrix B, where all the diagonals and the upper subdiagonals are positive, and its transpose BT , it is shown in the recent paper [4] that quantities JM(B) ≡ Tr(((BT B)M)−1) (M = 1, 2, . . . ) gives a sequence of lower bounds θM(B) of the minimal singular value of B through θM(B) ≡ (JM(B)). In [4], simple recurrence relations for computing all the diagonals of ((BT ...

A Differential Equation Approach to the Singular Value Decomposition of Bidiagonal Matrices

We consider the problem of approximating the singular value decomposition of a bidiagonal matrix by a one-parameter family of differentiable matrix flows. It is shown that this approach can be fully expressed as an autonomous, homogeneous, and cubic dynamical system. Asymptotic behavior is justified by the established theory of the Toda lattice.

Positive solutions for discrete fractional initial value problem

‎‎In this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz f...

Admissibility analysis for discrete-time singular systems with time-varying delays by adopting the state-space Takagi-Sugeno fuzzy model

This paper is pertained with the problem of admissibility analysis of uncertain discrete-time nonlinear singular systems by adopting the state-space Takagi-Sugeno fuzzy model with time-delays and norm-bounded parameter uncertainties. Lyapunov Krasovskii functionals are constructed to obtain delay-dependent stability condition in terms of linear matrix inequalities, which is dependent on the low...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces