Adaptive Wavelet Discretization Of Tensor Products In H Tucker Format

Download or read book Adaptive Wavelet Discretization of Tensor Products in H-Tucker Format written by Mazen Ali and published by . This book was released on 2014 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In previous work, the solution to a system of coupled parabolic PDEs, modeling the price of a CDO, was approximated numerically. Due to the nature of the problem, the system involved a large number of equations such that the parameters cannot be stored explicitly. The authors combined the data sparse H-Tucker storage format with the Galerkin method to approximate the solution, using wavelets for the space discretization together with time stepping (Method of Lines). The aforementioned approximation is of the linear kind, i.e., using a nonadaptive method. In this work, three methods for solving such systems adaptively are presented, together with a convergence and complexity analysis. The best choice of the method among the three, in general, depends on the particular application. It is shown that (quasi- )optimality is not achieved in the classical sense for adaptive methods, since it, in general, relies on the H-Tucker structure."--Abstract, page iii.