News

We introduce the concept of samplets by transferring the construction of Tausch-White wavelets to scattered data. This way, we obtain a multiresolution analysis tailored to discrete data which directly enables data compression, feature detection and adaptivity. The cost for constructing the samplet basis and for the fast samplet transfrom, respectively, is O(N), where N is the number of data points.                                                                                                                                              Samplets with vanishing moments can be used to compress kernel matrices, arising, for instance, in kernel based learning and scattered data approximation. The result are sparse matrices with only O(N log N) relevant entries. We provide estimates for the compression error and present an algorithm that computes the compressed kernel matrix with computaional cost O(N log N). The accuracy of the approximation is controlled by the number of vanishing moments.    Since addition, multiplication and inverses of kernel matrices are compressible, too, we derive an efficient kernel matrix algebra, which enables in particular series expansions and contour integrals wo access, numerically and approximately in a data-sparse format, more complicated matrix functions such as A^alpha and exp(A). Numerical results are presented to quantify and quality our findings. 

The guest talk will take place on June 13, 2023 from 4:30 - 5:30 pm in H 19 (NW II).