  The problems of computational data processing involving regression,
interpolation, reconstruction and imputation for multidimensional big datasets
are becoming more important these days, because of the availability of data and
their widely spread usage in business, technological, scientific and other
applications. The existing methods often have limitations, which either do not
allow, or make it difficult to accomplish many data processing tasks. The
problems usually relate to algorithm accuracy, applicability, performance
(computational and algorithmic), demands for computational resources, both in
terms of power and memory, and difficulty working with high dimensions. Here,
we propose a new concept and introduce two methods, which use local area
predictors (input data) for finding outcomes. One method uses the gradient
based approach, while the second one employs an introduced family of smooth
approximating functions. The new methods are free from many drawbacks of
existing approaches. They are practical, have very wide range of applicability,
provide high accuracy, excellent computational performance, fit for parallel
computing, and very well suited for processing high dimension big data. The
methods also provide multidimensional outcome, when needed. We present
numerical examples of up to one hundred dimensions, and report in detail
performance characteristics and various properties of new methods.
