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111.
K. Mørken 《Constructive Approximation》1991,7(1):195-208
In this paper it is shown how the algebraic product of two spline functions, each represented in terms of B-splines, can again be represented as a linear combination of suitable B-splines. As a corollary to this result we obtain an explicit representation of a given B-spline function in terms of B-splines of some arbitrary higher degree. This generalizes some known results for raising the degree by one. Recurrence relations for both products and degree raising are established that may be useful for computation.Communicated by Larry L. Schumaker. 相似文献
112.
The paper analyses the convergence of sequences of control polygons produced by a binary subdivision scheme of the form
相似文献
113.
The problem of computing the dimension of spaces of splines whose elements are piecewise polynomials of degreed withr continuous derivatives globally has attracted a great deal of attention recently. We contribute to this theory by obtaining dimension formulae for certain spaces of super splines, including the case where varying amounts of additional smoothness is enforced at each vertex. We also explicitly construct minimally supported bases for the spaces. The main tool is the Bernstein-Bézier method.Communicated by Klaus Höllig. 相似文献
114.
Jaromír Šimša 《Aequationes Mathematicae》1992,43(2-3):248-263
Summary We consider the problem of the best approximation of a given functionh L
2
(X × Y) by sums
k=1
n
f
k
f
k, with a prescribed numbern of products of arbitrary functionsf
k L
2
(X) andg
k L
2
(Y). As a co-product we develop a new proof of the Hilbert—Schmidt decomposition theorem for functions lying inL
2
(X × Y). 相似文献
115.
We establish a result related to a theorem of de Boor and Jia [1]. Their theorem, in turn, corrected and extended a result of Fix and Strang [5] concerning controlled approximation. In our result, the approximating functions are not required to have compact support, but satisfy instead conditions on their behavior at . Our theorem includes some recent results of Jackson [6] and is closely related to the work of Buhmann [2].Communicated by Carl de Boor 相似文献
116.
The approximation order provided by a directed set {S
h
}
h>0 of spaces, each spanned by thehZ
d
-translates of one function, is analyzed. The nearoptimal approximants of [R2] from eachs
h
to the exponential functions are used to establish upper bounds on the approximation order. These approximants are also used on the Fourier transform domain to yield approximations for other smooth functions, and thereby provide lower bounds on the approximation order. As a special case, the classical Strang-Fix conditions are extended to bounded summable generating functions.The second part of the paper consists of a detailed account of various applications of these general results to spline and radial function theory. Emphasis is given to the case when the scale {s
h
} is obtained froms
1 by means other than dilation. This includes the derivation of spectral approximation orders associated with smooth positive definite generating functions. 相似文献
117.
Sharp Remez-, Nikolskii-, and Markov-type inequalities are proved for functions of the form
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