An optimal bound for inverses of triangular matrices with monotone entries |
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Authors: | Kenneth S. Berenhaut Richard T. Guy Nathaniel G. Vish |
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Affiliation: | 1. Department of Mathematics , Wake Forest University , Winston-Salem, NC 27109, USA berenhks@wfu.edu;3. Department of Mathematics , Wake Forest University , Winston-Salem, NC 27109, USA |
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Abstract: | This article provides a new bound for 1-norms of inverses of positive triangular matrices with monotonic column entries. The main theorem refines a recent inequality established in Vecchio and Mallik [Bounds on the inverses of non-negative lower triangular Toeplitz matrices with monotonicity properties, Linear Multilinear Alg., 55 (2007), pp. 365–379]. The results are shown to be in a sense best possible under the given constraints. |
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Keywords: | inverse matrix monotone entries triangular matrix recurrence relations optimal bound |
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