  We propose a new partial decoding algorithm for $h$-interleaved one-point
Hermitian codes that can decode-under certain assumptions-an error of relative
weight up to $1-(\tfrac{k+g}{n})^{\frac{h}{h+1}}$, where $k$ is the dimension,
$n$ the length, and $g$ the genus of the code. Simulation results for various
parameters indicate that the new decoder achieves this maximal decoding radius
with high probability. The algorithm is based on a recent generalization of
Rosenkilde's improved power decoder to interleaved Reed-Solomon codes, does not
require an expensive root-finding step, and improves upon the previous best
decoding radius by Kampf at all rates. In the special case $h=1$, we obtain an
adaption of the improved power decoding algorithm to one-point Hermitian codes,
which for all simulated parameters achieves a similar observed failure
probability as the Guruswami-Sudan decoder above the latter's guaranteed
decoding radius.
