Masters Theses

Mazen Ali

Keywords and Phrases

adaptive; CDO; h-tucker; numerical; quasi-optimal; wavelets

Abstract

"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.

Advisor(s)

Bohner, Martin, 1966-

Committee Member(s)

Adekpedjou, Akim
Urban, Karsten

Department(s)

Mathematics and Statistics

Degree Name

M.S. in Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Summer 2014

Pagination

xii, 114 pages

Note about bibliography

Includes bibliographical references (pages 110-113).

Rights

© 2014 Mazen Ali, All rights reserved.

Document Type

Thesis - Open Access

File Type

text

Language

English

Subject Headings

Tensor products
Wavelets (Mathematics) -- Numerical analysis

Thesis Number

T 10502

Electronic OCLC #

894577460

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Included in

Mathematics Commons

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