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The problems of computational data processing involving regression,interpolation, reconstruction and imputation for multidimensional big datasetsare becoming more important these days, because of the availability of data andtheir widely spread usage in business, technological, scientific and otherapplications. The existing methods often have limitations, which either do notallow, or make it difficult to accomplish many data processing tasks. Theproblems usually relate to algorithm accuracy, applicability, performance(computational and algorithmic), demands for computational resources, both interms of power and memory, and difficulty working with high dimensions. Here,we propose a new concept and introduce two methods, which use local areapredictors (input data) for finding outcomes. One method uses the gradientbased approach, while the second one employs an introduced family of smoothapproximating functions. The new methods are free from many drawbacks ofexisting approaches. They are practical, have very wide range of applicability,provide high accuracy, excellent computational performance, fit for parallelcomputing, and very well suited for processing high dimension big data. Themethods also provide multidimensional outcome, when needed. We presentnumerical examples of up to one hundred dimensions, and report in detailperformance characteristics and various properties of new methods.

New reconstruction and data processing methods for regression and interpolation analysis of multidimensional big data