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We introduce and analyze the new range-separated (RS) canonical and Tucker tensor formats and apply them to numerical modeling of the arbitrarily distributed 3D long-range interaction potentials in multi-particle systems.
The main idea of the hybrid RS tensor formats is the independent low-rank representation of the localized and global parts in the target tensor which reduces the costs of related multi-linear algebra and enhances numerical treatment of many-particle interactions.
The reference interaction potential is precomputed in the form of a single low-rank canonical tensor on a 3D
The respective rank bounds provide theoretical justification of the new approach to summation of arbitrarily distributed interaction potentials. Agglomeration of the short range sum is reduced to the independent treatment of
The RS-canonical or RS-Tucker tensor representations simplify algebraic operations on the 3D potential sums arising in multi-dimensional data modeling by radial basis functions, in 3D integration and convolution, computation of gradients, forces and the interaction energy of a system etc., by reducing all of them to 1D calculations. In particular, we introduce the new regularized formulation for the Poisson-Boltzmann equation that may be useful for efficient computation of the electrostatic potential of proteins.