# Approximation-Degree-Based Interpolation: A New Interpolation Method

This paper introduces
the measure of approximate-degree and the concept of approximate-degree
function between numerical values, thus developing a new interpolation method
—— approximation-degree-based interpolation, i.e., AD interpolation.
One-dimensional AD interpolation is done directly by using correlative
interpolation formulas;

*n*(*n*>1)-dimensional AD interpolation is firstly separated into*n*parallel one-dimensional AD interpolation computations to do respectively, and then got results are synthesized by Sum-Times-Difference formula into a value as the result value of the*n*-dimensional interpolation. If the parallel processing is used, the efficiency of*n*-dimensional AD interpolation is almost the same as that of the one-dimensional AD interpolation. Thus it starts a feasible and convenient approach and provides an effective method for high-dimensional interpolations. Furthermore, if AD interpolation is introduced into machine learning, a new instance-based learning method is expected to be realized.