B1025
Title: Sparse polynomial prediction
Authors: Hugo Maruri - QMUL (United Kingdom) [presenting]
Abstract: In numerical analysis, sparse grids are point configurations that are used in stochastic finite element approximation, numerical integration and interpolation. The focus is on the construction of polynomial interpolator models in sparse grids. The proposal stems from the fact that a sparse grid is an echelon design with a hierarchical structure that identifies a single model. The model is then formulated and shown that it can be written using inclusion-exclusion formulae. At this point, efficient methodologies are deployed from the algebraic literature which can simplify considerably the computations. The methodology uses Betti numbers to reduce the number of terms in the inclusion-exclusion while achieving the same result as with exhaustive formulae.
