In this bachelor thesis, a method is introduced to improve the offline step of sparse grid density estimation with the combination technique. The developed approach exploits the geometrical properties of the subgrids in the combination scheme, to transform already decomposed corresponding system matrices. The transformation consists of a symmetric permutatation of the system matrix, aswell as the elementwise multiplication of a dimension blow-up factor. The former can be applied when two subgrids have level vectors, that are permutations of each other, while the latter yields an embedding into higher dimensions. The applicability is examined for the orthogonal decomposition into hessenberg form and the cholesky decomposition. For the orthogonal decomposition, the method has been implemented. Compared to the current implementation, it provides a speed up from cubic to quadratic time for the offline step of suitable component grids.     «

In this bachelor thesis, a method is introduced to improve the offline step of sparse grid density estimation with the combination technique. The developed approach exploits the geometrical properties of the subgrids in the combination scheme, to transform already decomposed corresponding system matrices. The transformation consists of a symmetric permutatation of the system matrix, aswell as the elementwise multiplication of a dimension blow-up factor. The former can be applied when two subgrid...     »