Computationally efficient method for multidimensional data interpolation

摘要

A method for interpolating multidimensional tabular data is developed herein. The main goals of the multidimensional interpolation scheme are to obtain second-derivative continuity across data points, and to have a computationally efficient method for obtaining function evaluations. These goals are accomplished by using multilinear interpolating functions (bilinear, trilinear, etc.) over most of the data set, and using higher-order polynomial surfaces in the vicinity of the data points to connect the multilinear surfaces in a smooth way. This provides second-derivative continuity, and since the majority of the data table is modeled with multilinear functions, the function evaluations are faster than when using higher-order polynomials. An additional feature of this method is that the interpolating functions are found locally rather than globally. This allows for N-dimensional tables to be handled very efficiently.