Numerical Evaluation of Reproducing Kernel Hilbert Space Inner Products

A new approach to numerically evaluate an inner product or a norm in an arbitrary reproducing kernel Hilbert space (RKHS) is considered. The proposed methodology enables us to approximate the RKHS inner product with the desired accuracy avoiding analytical expressions. Furthermore, its implementation is illustrated by means of some classic examples and compared with the standard iterative method provided by Weiner for this purpose. Finally, applications in both the problem of representing approximately second-order stochastic processes by means of series expansions and in the problem of signal detection are studied.