# zbMATH — the first resource for mathematics

On quasi-interpolation by radial basis functions with scattered centres. (English) Zbl 0824.41010
Summary: Approximation by radial basis functions with “quasi-uniformly” distributed centres in $$\mathbb{R}^ d$$ 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 investigted. It is shown that the quasi-interpolant reproduces polynomials and gives approximation orders identical to those in the uniform square-grid case.

##### MSC:
 41A15 Spline approximation 41A63 Multidimensional problems 41A25 Rate of convergence, degree of approximation 65D15 Algorithms for approximation of functions 41A30 Approximation by other special function classes 65D07 Numerical computation using splines 65D10 Numerical smoothing, curve fitting