Novel meshes for multivariate interpolation and approximation

A rapid increase in the quantity of data available is allowing all fields of science to generate more accurate models of multivariate phenomena. Regression and interpolation become challenging when the dimension of data is large, especially while maintaining tractable computational complexity. This paper proposes three novel techniques for multivariate interpolation and regression that each have polynomial complexity with respect to number of instances (points) and number of attributes (dimension). Initial results suggest that these techniques are capable of effectively modeling multivariate phenomena while maintaining flexibility in different application domains.