Need to accurately interpolate scattered data in multiple dimensions? This paper introduces a method for constructing smooth functions of two or more variables that interpolate data values at arbitrarily distributed points. While Shepard's method offers low storage and easy generalization, it suffers from low accuracy and high computational cost. This research presents a modified Shepard's method achieving accuracy comparable to other local methods without sacrificing advantages. A cell method for nearest-neighbor searching further improves computational efficiency. Test results for two and three independent variables demonstrate the method's effectiveness, providing an efficient solution for multivariate interpolation problems.
As ACM Transactions on Mathematical Software publishes research on algorithms and software for mathematical problems, this paper is highly relevant. The introduction of a modified Shepard's method addresses the challenge of multivariate interpolation, offering improved accuracy and efficiency, which directly contributes to the journal's focus on mathematical software.