On rational B-splines with prescribed poles
نویسندگان
چکیده
منابع مشابه
Expo-rational B-splines Expo-rational B-splines Expo-rational B-splines
A new type of B-spline the expo-rational B-spline is introduced. The heuristic motivation for its introduction comes from important similarities in several celebrated mathematical constructions originating in approximation theory, differential geometry and operator theory. The main result of the paper is the derivation of an Edgeworth and a steepest-descent/saddlepoint asymptotic expansion whic...
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Firstly, we introduce a new type of weight functions named as N-doubling weights, which is an essential generalization of the well known doubling weights. Secondly, we establish a weighted Turán type inequality with N-doubling weights and a Nikolskii-Turán type inequality for rational functions with prescribed poles. Our results generalize some known Turán type inequality both for polynomials a...
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The concept of expo-rational B-spline (ERBS) was introduced in [6] where the ’superproperties’ of ERBS were studied for the first time. In 2006 the first author of the present paper proposed a framework for the generalization of ERBS, the so-called generalized ERBS (GERBS), and considered one important instance of GERBS, the so-called Euler Beta-function B-splines (BFBS) which offered a good tr...
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In this note a recurrence relation for rational B-splines is presented. Using this formula, it is possible to write a rational spline in terms of normalized rational B-splines of lower order, with certain rational coeecients; these coincide with that generated by the well-known "rational version of the de Boor algorithm" based on knot-insertion Farin '88], Farin '89]. A modiied relation is pres...
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We introduce the several possible ”NUERBS” forms of expo-rational B-splines, and discuss the hierarchy of these forms in the univariate case. We give some first instances of exploration of properties of the expo-rational NUERBS which depend not only on the NUERBS weights but also on the intrinsic parameters of the expo-rational Bsplines.
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2004
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(03)00922-1