Keywords and Phrases
adaptive; CDO; h-tucker; numerical; quasi-optimal; wavelets
"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.
Bohner, Martin, 1966-
Mathematics and Statistics
M.S. in Mathematics
Missouri University of Science and Technology
xii, 114 pages
© 2014 Mazen Ali, All rights reserved.
Thesis - Open Access
Library of Congress Subject Headings
Wavelets (Mathematics) -- Numerical analysis
Electronic OCLC #
Ali, Mazen, "Adaptive wavelet discretization of tensor products in H-Tucker format" (2014). Masters Theses. 7294.