SPARSE APPROXIMATION USING l(1)-l(2) MINIMIZATION AND ITS APPLICATION TO STOCHASTIC COLLOCATION

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We discuss the properties of sparse approximation using l(1)-l(2) minimization. We present several theoretical estimates regarding its recoverability for both sparse and nonsparse signals. We then apply the method to sparse orthogonal polynomial approximations for stochastic collocation, with a focus on the use of Legendre polynomials. We study the recoverability of both the standard l(1)-l(2) minimization and Chebyshev weighted l(1)-l(2) minimization. It is noted that the Chebyshev weighted version is advantageous only at low dimensions, whereas the standard nonweighted version is preferred in high dimensions. Various numerical examples are presented to verify the theoretical findings.
Publisher
SIAM PUBLICATIONS
Issue Date
2017
Language
English
Article Type
Article
Citation

SIAM JOURNAL ON SCIENTIFIC COMPUTING, v.39, no.1, pp.A229 - A254

ISSN
1064-8275
DOI
10.1137/15M103947X
URI
http://hdl.handle.net/10203/297254
Appears in Collection
MA-Journal Papers(저널논문)
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