Name
Abstract | ||
|---|---|---|
In this paper we are concerned with the construction and use of wavelet approximation spaces for the fast evaluation of integral expressions. The spaces are based on biorthogonal anisotropic tensor product wavelets. We introduce sparse grid (hyperbolic cross) approximation spaces which are adapted not only to the smoothness of the kernel but also to the norm in which the error is measured. Furthermore, we introduce compression schemes for the corresponding discretizations. Numerical examples for the Laplace equation with Dirichlet boundary conditions and an additional integral term with a smooth kernel demonstrate the validity of our theoretical results. |
Year | DOI | Venue |
|---|---|---|
2002 | 10.1137/S0036142900375426 | SIAM Journal on Numerical Analysis |
Keywords | Field | DocType |
additional integral term,wavelet approximation space,sparse grids,integral expression,biorthogonal anisotropic tensor product,integral operators,approximation space,dirichlet boundary condition,laplace equation,smooth kernel,corresponding discretizations,compression scheme,compression,integral equations | Tensor product,Mathematical optimization,Mathematical analysis,Dirichlet boundary condition,Integral equation,Laplace's equation,Biorthogonal system,Sparse grid,Mathematics,Biorthogonal wavelet,Hyperbolic partial differential equation | Journal |
Volume | Issue | ISSN |
39 | 5 | 0036-1429 |
Citations | PageRank | References |
1 | 0.41 | 4 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Stephan Knapek | 1 | 22 | 3.00 |
| Frank Koster | 2 | 1 | 2.43 |