Bounds for fourth-order [0, 1] difference equations

Authors:
Kenneth S. Berenhaut;Benjamin G. Gibson;Jonathan H. Newman;Jacob F. Anderson
Affiliations:
Wake Forest University, Department of Mathematics, Winston-Salem, NC 27109, United States;Wake Forest University, Department of Mathematics, Winston-Salem, NC 27109, United States;Wake Forest University, Department of Mathematics, Winston-Salem, NC 27109, United States;The University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States
Venue:
Computers & Mathematics with Applications
Year:
2007

Citing 7
Cited 0

Asymptotic enumeration methods

Handbook of combinatorics (vol. 2)
Condition Numbers of Random Triangular Matrices

SIAM Journal on Matrix Analysis and Applications
On the solution of a linear homogeneous difference equation with variable coefficients

SIAM Journal on Mathematical Analysis
Random Fibonacci sequences and the number 1.13198824…

Mathematics of Computation
Computing Yapunov constants for random recurrences with smooth coefficients

Journal of Computational and Applied Mathematics
Lyapunov exponents from random fibonacci sequences to the lorenz equations

Lyapunov exponents from random fibonacci sequences to the lorenz equations
Second-order bounds for linear recurrences with negative coefficients

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.09

Visualization

Abstract

This note examines bounds for fourth-order linear difference equations with coefficients restricted to the unit interval. It is shown that all solutions are of order strictly less than (3/2)^n. The bound is shown to be nearly best possible. Applications to zero-one banded matrices are also discussed.