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Multidimensional Spline Approximation
SIAM Journal on Numerical Analysis, 1980Summary: We give direct and inverse estimates for multivariate spline approximation. The direct estimates rest on new results for local polynomial approximation which generalize the work of Brudnyi and Bramble-Hilbert. The inverse estimates are multivariate extensions of one variable ideas.
Dahmen, W., De Vore, R., Scherer, K.
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SPLINE APPROXIMATIONS ON MANIFOLDS
International Journal of Wavelets, Multiresolution and Information Processing, 2006A method of construction of the local approximations in the case of functions defined on n-dimensional (n ≥ 1) smooth manifold with boundary is proposed. In particular, spline and finite-element methods on manifold are discussed. Nondegenerate simplicial subdivision of the manifold is introduced and a simple method for evaluations of approach is ...
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Monotone Approximation by Splines
SIAM Journal on Mathematical Analysis, 1977We prove Jackson type estimates for the approximation of monotone nondecreasing functions by monotone nondecreasing splines with equally spaced knots. Our results are of the same order as the Jackson type estimates for unconstrained approximation by splines with equally spaced knots.
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NURBS APPROXIMATION OF A-SPLINES AND A-PATCHES
International Journal of Computational Geometry & Applications, 2003Given A-spline curves and A-patch surfaces that are implicitly defined on triangles and tetrahedra, we determine their NURBS representations. We provide a trimmed NURBS form for A-spline curves and a parametric tensor-product NURBS form for A-patch surfaces. We concentrate on cubic A-patches, providing a C1-continuous surface that interpolates a given
Chandrajit L. Bajaj +3 more
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Convex Approximation by Splines
SIAM Journal on Mathematical Analysis, 1981Jackson type estimates are obtained for the approximation of convex functions by convex splines with equally spaced knots. The results are of the same order as the Jackson type estimates for unconstrained approximation by splines with equally spaced knots.
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Approximation by Minimal Splines
Journal of Mathematical Sciences, 2013The author gives an abstract result about the rest of Lagrange type interpolation splines. This result applies to a different method used by the author in previous results on the same subject method.
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Approximation based on elliptic splines
International Journal of Wavelets, Multiresolution and Information Processing, 2014In this paper, we study the elliptic splines which include the well-known polyharmonic B-splines. We analyze their Fourier transforms, decay behaviors and polynomial reproducing properties. We also study the order of approximation in Sobolev spaces and consider their characterizations of Besov spaces by the scale projection operators, quasi ...
Zhuyuan Yang, Zongwen Yang
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2010
In this chapter we want to give a taste to the reader of the wide area of approximation theory. This is a very large subject, ranging from analytical to even engineering-oriented topics. We merely point out a few facts more closely related to our main treatment. We refer to [70] for a review of these topics.
Corrado De Concini, Claudio Procesi
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In this chapter we want to give a taste to the reader of the wide area of approximation theory. This is a very large subject, ranging from analytical to even engineering-oriented topics. We merely point out a few facts more closely related to our main treatment. We refer to [70] for a review of these topics.
Corrado De Concini, Claudio Procesi
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Approximation by Discrete GB-Splines
Numerical Algorithms, 2001Discrete generalized splines are continuous piecewise defined functions which meet some smoothness conditions for the first and second divided difference at the knots. They are a generalization both of smooth generalized splines and classic discrete cubic splines. The paper is devoted to the study of generalized splines.
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On the approximation power of bivariate splines
Advances in Computational Mathematics, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ming-Jun Lai, Larry L. Schumaker
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