In the present paper we will introduce a new approach to multivariate interpolation by employing polyharmonic functions as interpolants, i.e. by solutions of higher order elliptic equations. We assume that the data arise from $C^{ \infty}$ or analytic functions in the ball $B_{ R}.$ We prove two main results on the interpolation of $C^{ \infty}$ or analytic functions $f$ in the ball $B_{ R}$ by polyharmonic functions $h$ of a given order of polyharmonicity $p.$
Categories: math.NA math.FA