Sparse polynomial prediction

Abstract In numerical analysis, sparse grids are point configurations used in stochastic finite element approximation, integration and interpolation. This paper is concerned with the construction of polynomial interpolator models grids. Our proposal stems from fact that a grid an echelon design hierarchical structure identifies single model. We then formulate model show it can be written using inclusion–exclusion formulæ. At this point, we deploy efficient methodologies algebraic literature simplify considerably computations. The methodology uses Betti numbers to reduce number terms while achieving same result as exhaustive