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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… (More)
This short note provides an improvement on a recent result of Vecchio on a norm bound for the inverse of a lower triangular Toeplitz matrix with nonnegative entries. A sharper asymptotic bound is obtained in addition to a version for matrices of finite order. The results are shown to be nearly best possible under the given constraints. 1. Introduction. This… (More)
This paper gives optimal bounds for second order linear recurrences with coefficients bounded in negative intervals. The results involve maximal products over integer partitions. A closed form is given for the negative unit interval case.