Adaptive Sparse Grids with Nonlinear Basis in Interval Problems for Dynamical Systems
Alexander Yu. Morozov,
Dmitry L. Reviznikov
Abstract:Problems with interval uncertainties arise in many applied fields. The authors have earlier developed, tested, and proved an adaptive interpolation algorithm for solving this class of problems. The algorithm’s idea consists of constructing a piecewise polynomial function that interpolates the dependence of the problem solution on point values of interval parameters. The classical version of the algorithm uses polynomial full grid interpolation and, with a large number of uncertainties, the algorithm becomes di… Show more
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