Compressive sampling has been widely used for sparse polynomial chaos (PC)approximation of stochastic functions. The recovery accuracy of compressivesampling depends on the coherence properties of measurement matrix. In thispaper, we consider preconditioning the measurement matrix. Premultiplying alinear equation system by a non-singular matrix results in an equivalentequation system, but it can impact the coherence properties of preconditionedmeasurement matrix and lead to a different recovery accuracy. In this work, wepropose a preconditioning scheme that significantly improves the coherenceproperties of measurement matrix, and using theoretical motivations andnumerical examples highlight the promise of the proposed approach in improvingthe accuracy of estimated polynomial chaos expansions.
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