Second-order bounds for linear recurrences with negative coefficients

Authors:
Kenneth S. Berenhaut;Daniel C. Morton
Affiliations:
Wake Forest University, Department of Mathematics, Winston-Salem, NC 27109, USA;Wake Forest University, Department of Mathematics, Winston-Salem, NC 27109, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

This paper introduces a generalization of Fibonacci and Pell polynomials in order to obtain optimal second-order bounds for general linear recurrences with negative coefficients. An important aspect of the derived bounds is that they are applicable and easily computable. The results imply bounds on all entries in inverses of triangular matrices as well as on coefficients of reciprocals of power series.