Abstract
Motivated by uncertainty quantification and compressed sensing, we build up in this paper the framework for sparse interpolation. The main contribution of this work is twofold: (i) we investigate the theoretical limit of the number of unisolvent points for sparse interpolation under a general setting, and explore the relation between the classical interpolation and the sparse interpolation; (ii) we discuss the design of the interpolation points for the sparse multivariate polynomial expansions, for which the possible applications include uncertainty quantification and compressed sensing. Unlike the traditional random sampling method, we present in this paper a deterministic method to produce the interpolation points, and show its performance with $\ell_1$ minimization by analyzing the mutual incoherence of the interpolation matrix. Numerical experiments show that the deterministic points have a similar performance to that of the random points.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
