Norms of inverses and condition numbers for matrices associated with scattered data

AbstractFor interpolation matrices arising in connection with translates of a conditionally negative definite, radially symmetric Rs-function of order 1, we give a general method for obtaining bounds both on the norm of the inverse of the interpolation matrix and on the condition number of that matrix. We apply our method to obtain these bounds in several cases, including those associated with the functions √1 + ∥x∥22andlog(1 + ∥x∥22)