Continued fraction expansions of real powers of positive definite matrices with applications to matrix means

الملخص EN

The aim of this paper is to provide some results and applications for continued fractions with matrix arguments.

First, we introduce a continued fraction expansion of Aα where A is a positive definite matrix and α a positive real.

Then we provide an application to matrix means (defined below), which makes their computation practical as well as efficient.

At the end, some numerical examples are discussed.