  The main purpose of this work is the one of providing an efficient scheme for
constructing reduced interpolation models for kernel bases. In literature such
problem is mainly addressed via the well-established knot insertion or knot
removal schemes. Such iterative strategies are usually quite demanding from a
computational point of view and our goal is to study an efficient
implementation for data removal approaches, namely Efficient Reduced Basis
Algorithm (ERBA). Focusing on kernel-based interpolation, the algorithm makes
use of two iterative rules for removing data. The former, called ERBA-r, is
based on classical residual evaluations. The latter, namely ERBA-p, is
independent of the function values and relies on error bounds defined by the
power function. In both cases, inspired by the so-called extended Rippa's
algorithm, our ERBA takes advantage of a fast implementation.
