In this paper, the problem of efficient grid-based computation of the two-electron integrals (TEI) in a general basis is considered. We introduce the novel multiple tensor factorizations of the TEI unfolding matrix which decrease the computational demands for the evaluation of TEI in several aspects. Using the reduced higher-order SVD the redundancy-free product-basis set is constructed that di...

Tropical Newton-Puiseux polynomials, defined as piece-wise linear functions with rational coefficients of the variables, play a role tropical algebraic functions. We provide explicit formulas for polynomials being zeroes univariate polynomial parametric coefficients.

Based on the geometry of a radial function, sequence approximations for arcsine, arccosine and arctangent are detailed. The arcsine sharp at points zero one. Convergence is proved convergence significantly better than Taylor series arguments approaching established can be utilized as basis Newton-Raphson iteration analytical approximations, modest complexity, with relative error bounds order 10...

The parabolic partial differential equation arises in many application of technologies. In this paper, we propose an approximate method for solution of the heat and advection-diffusion equations using Laguerre-Gaussians radial basis functions (LG-RBFs). The results of numerical experiments are compared with the other radial basis functions and the results of other schemes to confirm the validit...

The Cahn–Hilliard (CH) equation is a time-dependent fourth-order partial differential equation (PDE). When solving the CH equation via the finite element method (FEM), the domain is discretized by C-continuous basis functions or the equation is split into a pair of second-order PDEs, and discretized via C-continuous basis functions. In the current work, a quantitative comparison between C Hermi...

This paper investigates inexact Newton methods for solving systems of nonsmooth equations. We de ne two inexact Newton methods for locally Lipschitz functions and we prove local (linear and superlinear) convergence results under the assumptions of semismoothness and BD-regularity at the solution. We introduce a globally convergent inexact iteration function based method. We discuss implementati...