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121.
Abstract. We propose C
1
Hermite interpolants generated by the general subdivision scheme introduced by Merrien [17] and satisfying monotonicity
or convexity constraints. For arbitrary values and slopes of a given function f at the end-points of a bounded interval, which are compatible with the contraints, the given algorithms construct shape-preserving
interpolants. Moreover, these algorithms are quite simple and fast as well as adapted to CAGD. We also give error estimates
in the case of interpolation of smooth functions. 相似文献
122.
Quasi-interpolation is very useful in the study of the approximation theory and its applications, since the method can yield solutions directly and does not require solving any linear system of equations. However, quasi-interpolation is usually discussed only for gridded data in the literature. In this paper we shall introduce a generalized Strang–Fix condition, which is related to nonstationary quasi-interpolation. Based on the discussion of the generalized Strang–Fix condition we shall generalize our quasi-interpolation scheme for multivariate scattered data, too.
AMS subject classification 41A63, 41A25, 65D10Zong Min Wu: Supported by NSFC No. 19971017 and NOYG No. 10125102. 相似文献
123.
The application of light sectioning to the accurate measurement of a rail cross-section, from a train moving at high speed, is described. The intensity distribution through the thickness of the illuminating light sheet is deliberately graded, allowing the shape of the object to be recovered more accurately by interpolation of the sampled image. Rail profiles are extracted with a definition approximately ten-times better than that of the sampled image. 相似文献
124.
WANG Xinghua~ 《中国科学A辑(英文版)》2005,48(1)
The best quadrature formula has been found in the following sense:for afunction whose norm of the second derivative is bounded by a given constant and thebest quadrature formula for the approximate evaluation of integration of that function canminimize the worst possible error if the values of the function and its derivative at certainnodes are known.The best interpolation formula used to get the quadrature formula aboveis also found.Moreover,we compare the best quadrature formula with the open compoundcorrected trapezoidal formula by theoretical analysis and stochastic experiments. 相似文献
125.
M. Marx 《Algebra Universalis》2000,43(1):41-49
For every finite n > 1, the embedding property fails in the class of all n-dimensional cylindric type algebras which satisfy the following. Their boolean reducts are boolean algebras and two of the
cylindrifications are normal, additive and commute. This result also holds for all subclasses containing the representable
n-dimensional cylindric algebras. This considerably strengthens a result of S. Comer on CA
n
and provides a strong counterexample for interpolation in finite variable fragments of first order logic. We provide a new
modern proof, using an argument inspired by modal logic.
February 22, 1999. 相似文献
126.
Thomas Sauer 《Transactions of the American Mathematical Society》2001,353(6):2293-2308
The paper is concerned with a construction for H-bases of polynomial ideals without relying on term orders. The main ingredient is a homogeneous reduction algorithm which orthogonalizes leading terms instead of completely canceling them. This allows for an extension of Buchberger's algorithm to construct these H-bases algorithmically. In addition, the close connection of this approach to minimal degree interpolation, and in particular to the least interpolation scheme due to de Boor and Ron, is pointed out.
127.
128.
In this work,the well-known problem put forward by S N Bernstein in 1930 is studied in a deep step.An operator is constructed by revising double interpolation nodes.It is proved that the operator converges to arbitrary continuous functions uniformly and the convergence order is the best. 相似文献
129.
A new interface reconstruction method in 3D is presented. The method involves a conservative level‐contour reconstruction coupled to a cubic‐Bézier interpolation. The use of the proposed piecewise linear interface calculation (PLIC) reconstruction scheme coupled to a multidimensional time integration provides solutions of second‐order spatial and temporal accuracy. The accuracy and efficiency of the proposed reconstruction algorithm are demonstrated through several tests, whose results are compared with those obtained with other recently proposed methods. An overall improvement in accuracy with respect to other recent methods has been achieved, along with a substantial reduction in the central processing unit time required. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
130.
Mathematical Notes - 相似文献