4,640 research outputs found
Generalized quadratic B-splines generated by Merrien subdivision algorithm and some applications
A new global basis of B-splines is defined in the space of generalized
quadratic splines (GQS) generated by Merrien subdivision algorithm. Then,
refinement equations for these B-splines and the associated corner-cutting
algorithm are given. Afterwards, several applications are presented. First a
global construction of monotonic and/or convex generalized splines
interpolating monotonic and/or convex data. Second, convergence of sequences of
control polygons to the graph of a GQS. Finally, a Lagrange interpolant and a
quasi-interpolant which are exact on the space of affine polynomials and whose
infinite norms are uniformly bounded independently of the partition.Comment: 2004-1
Estimation of a -monotone density: limit distribution theory and the spline connection
We study the asymptotic behavior of the Maximum Likelihood and Least Squares
Estimators of a -monotone density at a fixed point when .
We find that the th derivative of the estimators at converges at the
rate for . The limiting distribution depends
on an almost surely uniquely defined stochastic process that stays above
(below) the -fold integral of Brownian motion plus a deterministic drift
when is even (odd). Both the MLE and LSE are known to be splines of degree
with simple knots. Establishing the order of the random gap
, where denote two successive knots, is a key
ingredient of the proof of the main results. We show that this ``gap problem''
can be solved if a conjecture about the upper bound on the error in a
particular Hermite interpolation via odd-degree splines holds.Comment: Published in at http://dx.doi.org/10.1214/009053607000000262 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Splines and Wavelets on Geophysically Relevant Manifolds
Analysis on the unit sphere found many applications in
seismology, weather prediction, astrophysics, signal analysis, crystallography,
computer vision, computerized tomography, neuroscience, and statistics.
In the last two decades, the importance of these and other applications
triggered the development of various tools such as splines and wavelet bases
suitable for the unit spheres , and the
rotation group . Present paper is a summary of some of results of the
author and his collaborators on generalized (average) variational splines and
localized frames (wavelets) on compact Riemannian manifolds. The results are
illustrated by applications to Radon-type transforms on and
.Comment: The final publication is available at http://www.springerlink.co
Exact asymptotics of the optimal Lp-error of asymmetric linear spline approximation
In this paper we study the best asymmetric (sometimes also called penalized
or sign-sensitive) approximation in the metrics of the space , , of functions with nonnegative
Hessian by piecewise linear splines , generated by given
triangulations with elements. We find the exact asymptotic
behavior of optimal (over triangulations and splines error of such approximation as
Polynomial cubic splines with tension properties
In this paper we present a new class of spline functions with tension properties. These splines are composed by polynomial cubic pieces and therefore are conformal to the standard, NURBS based CAD/CAM systems
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