Extending Putzer's representation to all analytic matrix functions via omega matrix calculus
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Date
2021-12-07
Authors
Neto, Antonio Francisco
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We show that Putzer's method to calculate the matrix exponential in [28] can be generalized to compute an arbitrary matrix function defined by a convergent power series. The main technical tool for adapting Putzer's formulation to the general setting is the omega matrix calculus; that is, an extension of MacMahon's partition analysis to the realm of matrix calculus and the method in [6]. Several results in the literature are shown to be special cases of our general formalism, including the computation of the fractional matrix exponentials introduced by Rodrigo [30]. Our formulation is a much more general, direct, and conceptually simple method for computing analytic matrix functions. In our approach the recursive system of equations the base for Putzer's method is explicitly solved, and all we need to determine is the analytic matrix functions.
Description
Keywords
Putzer's method, Omega matrix calculus, Matrix valued convergent series, Mittag-Leffler function, Fractional calculus
Citation
Neto, A. F. (2021). Extending Putzer's representation to all analytic matrix functions via omega matrix calculus. <i>Electronic Journal of Differential Equations, 2021</i>(97), pp. 1-18.
Rights
Attribution 4.0 International