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Dive into the research topics where F. Kuijt is active.

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Featured researches published by F. Kuijt.


Computer Aided Geometric Design | 1999

Convexity preservation of the four-point interpolatory subdivision scheme

Nira Dyn; F. Kuijt; David Levin; Rudolf M.J. van Damme

In this note we examine the convexity preserving properties of the (linear) four-point interpolatory subdivision scheme of Dyn, Gregory and Levin when applied to functional univariate strictly convex data. Conditions on the tension parameter guaranteeing preservation of convexity are derived. These conditions depend on the initial data. The resulting scheme is the four-point scheme with tension parameter bounded from above by a bound smaller than 1/16. Thus the scheme generates C1 limit functions and has approximation order two.


Journal of Computational and Applied Mathematics | 1999

Monotonicity preserving interpolatory subdivision schemes

F. Kuijt; Rudolf M.J. van Damme

A class of local nonlinear stationary subdivision schemes that interpolate equidistant data and that preserve monotonicity in the data is examined. The limit function obtained after repeated application of these schemes exists and is monotone for arbitrary monotone initial data. Next a class of rational subdivision schemes is investigated. These schemes generate limit functions that are continuously differentiable for any strictly monotone data. The approximation order of the schemes is four. Some generalisations, such as preservation of piecewise monotonicity and application to homogeneous grid refinement, are briefly discussed.


Advances in Computational Mathematics | 2001

A Linear Approach to Shape Preserving Spline Approximation

F. Kuijt; Rudolf M.J. van Damme

This paper deals with the approximation of a given large scattered univariate or bivariate data set that possesses certain shape properties, such as convexity, monotonicity, and/or range restrictions. The data are approximated for instance by tensor-product B-splines preserving the shape characteristics present in the data.Shape preservation of the spline approximant is obtained by additional linear constraints. Constraints are constructed which are local linear sufficient conditions in the unknowns for convexity or monotonicity. In addition, it is attractive if the objective function of the resulting minimisation problem is also linear, as the problem can then be written as a linear programming problem. A special linear approach based on constrained least squares is presented, which in the case of large data reduces the complexity of the problem sets in contrast with that obtained for the usual ℓ2-norm as well as the ℓ∞-norm.An algorithm based on iterative knot insertion which generates a sequence of shape preserving approximants is given. It is investigated which linear objective functions are suited to obtain an efficient knot insertion method.


Constructive Approximation | 1998

Convexity preserving interpolatory subdivision schemes

F. Kuijt; R.M.J. van Damme


Journal of Approximation Theory | 2002

Shape Preserving Interpolatory Subdivision Schemes for Nonuniform Data

F. Kuijt; Rudolf M.J. van Damme


Archive | 1996

Smooth interpolation by a Convexity Preserving Nonlinear Subdivision Algorithm

F. Kuijt; Rudolf M.J. van Damme


Siam Journal on Control and Optimization | 1998

Stability of subdivision schemes

F. Kuijt; R.M.J. van Damme


Siam Journal on Control and Optimization | 1998

Shape preserving

F. Kuijt; R.M.J. van Damme


Memorandum Faculteit TW | 1998

C^2

F. Kuijt; Rudolf M.J. van Damme


Proceedings van het Symposium Wiskunde Toegepast, 33e Ned. Math. Congres | 1998

interpolatory subdivision schemes

F. Kuijt; Rudolf M.J. van Damme

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