Algorithm XXX: SHEPPACK: Modified Shepard Algorithm for Interpolation of Scattered Multivariate Data

Scattered data interpolation problems arise in many applications. Shepard’s method for constructing a global interpolant by blending local interpolants using local-support weight functions usually creates reasonable approximations. SHEPPACK is a Fortran 95 package containing five versions of the modified Shepard algorithm: quadratic (Fortran 95 translations of Algorithms 660, 661, and 798), cubic (Fortran 95 translation of Algorithm 791), and linear variations of the original Shepard algorithm. An option to the linear Shepard code is a statistically robust fit, intended to be used when the data is known to contain outliers. SHEPPACK also includes a hybrid robust piecewise linear estimation algorithm RIPPLE (residual initiated polynomial-time piecewise linear estimation) intended for data from piecewise linear functions in arbitrary dimension m. The main goal of SHEPPACK is to provide users with a single consistent package containing most existing polynomial variations of Shepard’s algorithm. The algorithms target data of different dimensions. The linear Shepard algorithm, robust linear Shepard algorithm, and RIPPLE are the only algorithms in the package that are applicable to arbitrary dimensional data.