MATHICSE Technical Report : A theoretical study of COmpRessed SolvING for advection-diffusion-reaction problems

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 infsup property, i.e., a combination of the classical inf-sup condition and the well-known restricted isometry property of compressed sensing.


Year:
Sep 10 2015
Publisher:
Écublens, MATHICSE
Keywords:
Note:
MATHICSE Technical Report Nr. 23.2015 September 2015
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 Record created 2019-01-25, last modified 2019-06-19

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