Convergence and C1 analysis of subdivision schemes on manifolds by proximity
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Convergence and C1 analysis of subdivision schemes on manifolds by proximity
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
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Replacing the median by a general M-estimator, we construct in this paper a host of variants of the robust nonlinear pyramid transforms proposed by Donoho and Yu [SIAM J. Math. Anal., 31 (2000) pp. 1030--1061]. Some of these new variants are more amenable to numerical implementations with provable properties when compared to the Donoho--Yu median-based pyramid transforms. At the crux of this generalized construction is the following result: the inverse problem of interpolating a univariate polynomial of degree n with n + 1 prescribed values for any given continuous M-estimator on n + 1 nonoverlapping intervals is a well-posed procedure. While the proof of this result is nonconstructive, we study the use of Newton methods for constructing such a polynomial interpolant and report numerical results in some test cases.