  This note carries three purposes involving our latest advances on the radial
basis function (RBF) approach. First, we will introduce a new scheme employing
the boundary knot method (BKM) to nonlinear convection-diffusion problem. It is
stressed that the new scheme directly results in a linear BKM formulation of
nonlinear problems by using response point-dependent RBFs, which can be solved
by any linear solver. Then we only need to solve a single nonlinear algebraic
equation for desirable unknown at some inner node of interest. The numerical
results demonstrate high accuracy and efficiency of this nonlinear BKM
strategy. Second, we extend the concepts of distance function, which include
time-space and variable transformation distance functions. Finally, we
demonstrate that if the nodes are symmetrically placed, the RBF coefficient
matrices have either centrosymmetric or skew centrosymmetric structures. The
factorization features of such matrices lead to a considerable reduction in the
RBF computing effort. A simple approach is also presented to reduce the
ill-conditioning of RBF interpolation matrices in general cases.
