  In kernel-based approximation, the tuning of the so-called shape parameter is
a fundamental step for achieving an accurate reconstruction. Recently, the
popular Rippa's algorithm [14] has been extended to a more general cross
validation setting. In this work, we propose a modification of such extension
with the aim of further reducing the computational costs. The resulting
Stochastic Extended Rippa's Algorithm (SERA) is first detailed and then tested
by means of various numerical experiments, which show its efficacy and
effectiveness in different approximation settings.
