Volume 44, Number 1, January-February 2010
|Page(s)||33 - 73|
|Published online||09 October 2009|
Wavelet compression of anisotropic integrodifferential operators on sparse tensor product spaces
ETH Zurich, Seminar for Applied Mathematics, 8092 Zurich, Switzerland. firstname.lastname@example.org
For a class of anisotropic integrodifferential operators arising as semigroup generators of Markov processes, we present a sparse tensor product wavelet compression scheme for the Galerkin finite element discretization of the corresponding integrodifferential equations u = f on [0,1]n with possibly large n. Under certain conditions on , the scheme is of essentially optimal and dimension independent complexity (h-1| log h |2(n-1)) without corrupting the convergence or smoothness requirements of the original sparse tensor finite element scheme. If the conditions on are not satisfied, the complexity can be bounded by (h-(1+ε)), where ε tends to zero with increasing number of the wavelets' vanishing moments. Here h denotes the width of the corresponding finite element mesh. The operators under consideration are assumed to be of non-negative (anisotropic) order and admit a non-standard kernel κ that can be singular on all secondary diagonals. Practical examples of such operators from Mathematical Finance are given and some numerical results are presented.
Mathematics Subject Classification: 47A20 / 65F50 / 65N12 / 65Y20 / 68Q25 / 45K05 / 65N30
Key words: Wavelet compression / sparse grids / anisotropic integrodifferential operators / norm equivalences
© EDP Sciences, SMAI, 2009
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.