Name
Abstract | ||
|---|---|---|
We present a theoretical analysis of the CORSING (COmpRessed SolvING) method for the numerical approximation of partial differential equations based on compressed sensing. In particular, we show that the best s-term approximation of the weak solution of a PDE with respect to a system of N trial functions, can be recovered via a Petrov-Galerkin approach using m << N test functions. This recovery is guaranteed if the local a-coherence associated with the bilinear form and the selected trial and test bases fulfills suitable decay properties. The fundamental tool of this analysis is the restricted inf-sup property, i.e., a combination of the classical inf-sup condition and the well-known restricted isometry property of compressed sensing. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1090/mcom/3209 | MATHEMATICS OF COMPUTATION |
Keywords | Field | DocType |
Compressed sensing,Petrov-Galerkin formulation,advection-diffusion-reaction equation,inf-sup property,local coherence | Mathematical optimization,Bilinear form,Mathematical analysis,Weak solution,Advection,Numerical approximation,Partial differential equation,Compressed sensing,Restricted isometry property,Mathematics | Journal |
Volume | Issue | ISSN |
87 | 309 | 0025-5718 |
Citations | PageRank | References |
1 | 0.41 | 14 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Simone Brugiapaglia | 1 | 1 | 3.45 |
| Fabio Nobile | 2 | 336 | 29.63 |
| Stefano Micheletti | 3 | 37 | 8.24 |
| Simona Perotto | 4 | 45 | 10.84 |