Codice | 42/2015 |
Titolo | A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems |
Data | 2015-09-07 |
Autore/i | Brugiapaglia, S.; Nobile, F.; Micheletti, S.; Perotto, S. |
Link | Download full text |
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 an orthonormal system of N trial functions, can be recovered via a Petrov-Galerkin approach using m ? N orthonormal 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. |
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