ON QUASI-INTERPOLATION BY RADIAL BASIS FUNCTIONS WITH SCATTERED CENTERS

Approximation by radial basis functions with ''quasi-uniformly'' distributed centres in R(d) is discussed. A construction of new polynomially decaying functions that span the approximation space is presented and the properties of the quasi-interpolation operator with these functions are investigated. It is shown that the quasi-interpolant reproduces polynomials and gives approximation orders identical to those in the uniform square-grid case.