排序方式: 共有88条查询结果,搜索用时 171 毫秒
1.
1引言 B样条在计算机图形学和几何建模等领域有着广泛的应用[3,8].在应用过程中,通常都需要对得到的模型进行修改以到达更好的效果.对于B样条曲线,利用节点插入算法可以有效地进行局部修改. 相似文献
2.
In this paper, the spline interpretations of Eulerian numbers and refined Eulerian numbers are presented. Many classical results about Eulerian numbers can follow from the properties of B-splines directly, and some new results about the refined Eulerian numbers and descent polynomials are also derived. Specifically, the explicit and recurrence formulas for the refined Eulerian numbers and descent polynomials are obtained. This paper also provides a new approach to study Eulerian numbers. 相似文献
3.
The paper describes a new space of variable degree polynomials. This space is isomorphic to ℙ6, possesses a Bernstein like basis and has generalized tension properties in the sense that, for limit values of the degrees,
its functions approximate quadratic polynomials. The corresponding space of C
3, variable degree splines is also studied. This spline space can be profitably used in the construction of shape preserving
curves or surfaces.
AMS subject classification (2000) 65D07, 65D17, 65D10 相似文献
4.
This paper studies systems of tensor-product functions for which the functions they span are monotonic in any direction when
their control nets are monotonic in that direction. It is shown that Bernstein polynomials and B-splines have this property
but that totally positive systems in general, such as certain trigonometric and rational bases, do not.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
5.
Gerlind Plonka 《Advances in Computational Mathematics》1995,3(1):1-22
The Fourier transforms of B-splines with multiple integer knots are shown to satisfy a simple recursion relation. This recursion
formula is applied to derive a generalized two-scale relation for B-splines with multiple knots. Furthermore, the structure
of the corresponding autocorrelation symbol is investigated.
In particular, it can be observed that the solvability of the cardinal Hermite spline interpolation problem for spline functions
of degree 2m+1 and defectr, first considered by Lipow and Schoenberg [9], is equivalent to the Riesz basis property of our B-splines with degreem and defectr. In this way we obtain a new, simple proof for the assertion that the cardinal Hermite spline interpolation problem in [9]
has a unique solution. 相似文献
6.
利用三次非均匀有理B样条,给出了一种构造局部插值曲线的方法,生成的插值曲线是C2连续的.曲线表示式中带有一个局部形状参数,随着一个局部形状参数值的增大,所给曲线将局部地接近插值点构成的控制多边形.基于三次非均匀有理B样条函数的局部单调性和一种保单调性的准则,给出了所给插值曲线的保单调性的条件. 相似文献
7.
Testing for additivity with B-splines 总被引:1,自引:0,他引:1
Regression splines are often used for fitting nonparametric functions, and they work especially well for additivity models. In this paper, we consider two simple tests of additivity: an adaptation of Tukey's one degree of freedom test and a nonparametric version of Rao's score test. While the Tukey-type test can detect most forms of the local non-additivity at the parametric rate of O(n-1/2), the score test is consistent for all alternative at a nonparametric rate. The asymptotic distribution of these test statistics is derived under both the null and local alternative hypotheses. A simulation study is conducted to compare their finite-sample performances with some existing kernel-based tests. The score test is found to have a good overall performance. 相似文献
8.
This paper applies difference operators to conditionally positive definite kernels in order to generate kernel
-splines that have fast decay towards infinity. Interpolation by these new kernels provides better condition of the linear system,
while the kernel -spline inherits the approximation orders from its native kernel. We proceed in two different ways: either the kernel -spline is constructed adaptively on the data knot set , or we use a fixed difference scheme and shift its associated kernel -spline around. In the latter case, the kernel -spline so obtained is strictly positive in general. Furthermore, special kernel -splines obtained by hexagonal second finite differences of multiquadrics are studied in more detail. We give suggestions
in order to get a consistent improvement of the condition of the interpolation matrix in applications. 相似文献
9.
Janet S. Kim Arnab Maity Raymond J. Carroll David Ruppert 《Journal of computational and graphical statistics》2018,27(1):234-244
We study additive function-on-function regression where the mean response at a particular time point depends on the time point itself, as well as the entire covariate trajectory. We develop a computationally efficient estimation methodology based on a novel combination of spline bases with an eigenbasis to represent the trivariate kernel function. We discuss prediction of a new response trajectory, propose an inference procedure that accounts for total variability in the predicted response curves, and construct pointwise prediction intervals. The estimation/inferential procedure accommodates realistic scenarios, such as correlated error structure as well as sparse and/or irregular designs. We investigate our methodology in finite sample size through simulations and two real data applications. Supplementary material for this article is available online. 相似文献
10.
Devendra Kumar Parvin Kumari 《Numerical Methods for Partial Differential Equations》2020,36(4):868-886
A numerical scheme for a class of singularly perturbed delay parabolic partial differential equations which has wide applications in the various branches of science and engineering is suggested. The solution of these problems exhibits a parabolic boundary layer on the lateral side of the rectangular domain which continuously depends on the perturbation parameter. For the small perturbation parameter, the standard numerical schemes for the solution of these problems fail to resolve the boundary layer(s) and the oscillations occur near the boundary layer. Thus, in this paper to resolve the boundary layer the extended cubic B-spline basis functions consisting of a free parameter λ are used on a fitted-mesh. The extended B-splines are the extension of classical B-splines. To find the best value of λ the optimization technique is adopted. The extended cubic B-splines are an advantage over the classical B-splines as for some optimized value of λ the solution obtained by the extended B-splines is better than the solution obtained by classical B-splines. The method is shown to be first-order accurate in t and almost the second-order accurate in x. It is also shown that this method is better than some existing methods. Several test problems are encountered to validate the theoretical results. 相似文献