TY - JOUR
T1 - Exact recovery of non-uniform splines from the projection onto spaces of algebraic polynomials
AU - Bendory, Tamir
AU - Dekel, Shai
AU - Feuer, Arie
PY - 2014/6
Y1 - 2014/6
N2 - In this work we consider the problem of recovering non-uniform splines from their projection onto spaces of algebraic polynomials. We show that under a certain Chebyshev-type separation condition on its knots, a spline whose inner-products with a polynomial basis and boundary conditions are known, can be recovered using Total Variation norm minimization. The proof of the uniqueness of the solution uses the method of 'dual' interpolating polynomials and is based on Candès and Fernandez-Granda (2014), where the theory was developed for trigonometric polynomials. We also show results for the multivariate case.
AB - In this work we consider the problem of recovering non-uniform splines from their projection onto spaces of algebraic polynomials. We show that under a certain Chebyshev-type separation condition on its knots, a spline whose inner-products with a polynomial basis and boundary conditions are known, can be recovered using Total Variation norm minimization. The proof of the uniqueness of the solution uses the method of 'dual' interpolating polynomials and is based on Candès and Fernandez-Granda (2014), where the theory was developed for trigonometric polynomials. We also show results for the multivariate case.
UR - http://www.scopus.com/inward/record.url?scp=84897870371&partnerID=8YFLogxK
U2 - 10.1016/j.jat.2014.03.001
DO - 10.1016/j.jat.2014.03.001
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AN - SCOPUS:84897870371
SN - 0021-9045
VL - 182
SP - 7
EP - 17
JO - Journal of Approximation Theory
JF - Journal of Approximation Theory
ER -