DEPRO, Universidade Federal de Ouro Preto
CEP 35.400-000, Ouro Preto, MG, Brazil
email: antonio.neto@ufop.edu.br
Antonio Francisco Neto
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.
Submitted March 3, 2021. Published December 7, 2021.
Math Subject Classifications: 15A16, 26A33.
Key Words: Putzer's method; omega matrix calculus;
matrix valued convergent series; Mittag-Leffler function; fractional calculus.
DOI: https://doi.org/10.58997/ejde.2021.97
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Antônio Francisco Neto DEPRO, Universidade Federal de Ouro Preto CEP 35.400-000, Ouro Preto, MG, Brazil email: antonio.neto@ufop.edu.br |
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