In practical numerical calculations as well as in their various
applications, the replacement of a truncated Taylor series by its
continued-fraction or Pad\'{e}-approximation equivalent proves to
have certain specific merits. The authors extend this idea from
the real numbers to matrices and describe the pattern and
illustrate the efficiency of its application using a sample of
examples ranging from the evaluation of a real power or of a
geometric mean of a matrix to the solution of a cubic matrix
equation.

MR2220054 Raissoulli, M.; Kacha, A.; Salhi, S.
Continued fraction expansions of real powers of positive definite
matrices with applications to matrix means.
Arab. J. Sci. Eng. Sect. A Sci. 31 (2006), no. 1, 41--55.
40A15 (47A63)