Polynomial representation of the matrix pth root functions and generalized Fibonacci sequences

Abstract : This study is devoted to the polynomial representation of the matrix pth root functions. The Fibonacci-Hörner decomposition of the matrix powers and some techniques arisen from properties of generalized Fibonacci sequences, notably the Binet formula, serves as a triggering factor to provide explicit formulas for the matrix pth roots. Special cases and illustrative numerical examples are given.
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Submitted on : Wednesday, October 4, 2017 - 1:53:22 PM
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Rajae Ben Taher, Youness Khatabi, Mustapha Rachidi. Polynomial representation of the matrix pth root functions and generalized Fibonacci sequences. 2017. ⟨hal-01610095⟩

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