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关于二元四次样条插值与逼近 总被引:4,自引:0,他引:4
文[1]中讨论了上的插值问题,其中的插值函数表达式用到被插值函数的二阶导数.本文进一步研究空间上的一类新的二元样条插值形式,其中仅用到插值函数的一阶导数.证明了该插值形式的唯一性与存在性,且不需要解高维的线性方程组.最后给出了逼近度问题. 相似文献
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1 引言和辅助引理 关于样条插值的渐近展开,目前已有许多工作,这些工作主要限于周期样条插值和基样条(cardinal spline)插值情形,它们不仅给出了插值误差的渐近展开,而且获得了逐项渐近展开。对于实际中应用最多的有限区间上的样条插值的渐近展开问题,由于受端点条件的影响,呈现十分复杂的局面。目前的工作只是获得了渐近展开结果,并未获得逐项渐近展开,且主要针对二、三次这类低次样条插值情形,考虑高次样条有良好的逼近性质,特别是其中四、五次样条插值在实际应用中被广泛采用,本文致力于研究四次样条插值问题,获得了其误差 相似文献
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一种四次有理插值样条及其逼近性质 总被引:3,自引:0,他引:3
1引言有理样条函数是多项式样条函数的一种自然推广,但由于有理样条空间的复杂性,所以有关它的研究成果不象多项式样条那样完美,许多问题还值得进一步的研究.近几十年来,有理插值样条,特别是有理三次有理插值样条,由于它们在曲线曲面设计中的应用,已有许多学者进行了深入研究,取得了一系列的成果(见[1]-[7]).但四次有理插值样条由于其构造所花费的计算量太大以及在使用上很不方便而让人们忽视了其重要的应用价值,因此很少有人研究他们.实际上,在某些情况下四次有理插值样条有其独特的应用效果,如文[8]建立的一种具有局部插值性质的分母为二次的四次有理样条,即一个剖分 相似文献
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关于双周期的二元四次样条插值 总被引:2,自引:0,他引:2
宣培才 《高等学校计算数学学报》1995,17(3):278-290
1 引 言 [1]给出了矩形区域在Ⅰ型三角剖分下双周期二元三次样条空间的维数,[2]利用B—网方法研究了矩形区域在Ⅱ型三角剖分下双周期二元三次样条的插值与逼近问题,不仅给出了空间的维数,且给出了插值样条的表达式和逼近度的估计。本文继续这一工作,讨论了双周期的二元四次样条插值的存在性、唯一性及其表达式和逼近度。本文所述方法不需解高维的线性方程组,具有计算简捷和逼近度较高的优点,因此有较大的实用性。 相似文献
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心磁图是根据人体心脏跳动产生的微弱磁场测量信号计算得到的医学图像,它较心电图诊断心脏疾病具有更高的灵敏度和准确性.为了提高心磁图的成像精度,通常需要对心磁检测数据进行插值处理.提供了双立方插值和二元三次样条插值两种插值方法,应用实例的结果表明,三次样条插值的效果比双立方插值效果好,基本能达到应用的要求. 相似文献
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本文讨论了二次样条插值的定解条件,在l_1模意义下给出了一类最佳二次样条插值的概念,以及寻找最佳二次样条插值的定解条件的方法.最后讨论了误差估计问题,并给出了实际算例. 相似文献
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构造了一种C^1连续的保单调的有理三次插值函数。由于函数表达式中含有调节参数,使得插值曲线更具灵活性。 相似文献
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一种有理三次保形插值样条王艳春,许有信(南京理工大学)(南京航空航天大学)ASHAPEPRESERVINGRATIONALCUBICINTERPOLATIONSPLINE¥WangYan-chun(NanjingUniversityofScience... 相似文献
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二元样条函数插值在计算几何与计算机辅助几何设计中有着重要的作用.本文给出了一种矩形剖分上二元线性样条函数进行Lagrange插值时插值适定结点组所满足的拓扑与几何性质,这种性质依赖于二元线性样条函数所决定的分片线性代数曲线. 相似文献
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分片代数曲线足经典代数曲线的推广.利用沿分片代数曲线插值以及分片代数曲线的Nother型定理,给出了一类构造拟贯穿剖分上的二元样条Lagrange插值适定结点组的一种方法,并给出具体算法与实例. 相似文献
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Günther Nürnberger Vera Rayevskaya Larry L. Schumaker Frank Zeilfelder 《Constructive Approximation》2005,23(1):33-59
We describe a method which can be used to interpolate
function values at a set of scattered points
in a planar domain using bivariate polynomial splines
of any prescribed smoothness.
The method starts with an arbitrary given triangulation
of the data points, and involves refining some of the
triangles with Clough-Tocher splits.
The construction of the interpolating splines requires
some additional function values at selected points in
the domain, but no derivatives are needed at any point.
Given n data points and a corresponding
initial triangulation, the interpolating spline can be
computed in just O(n) operations.
The interpolation method is local
and stable, and provides optimal order approximation of smooth
functions. 相似文献
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本文提出一种在局部坐标系下构造有理插值曲面的方法,它可用来解决曲面的"大挠度"问题。这种曲面逼近效果较佳,也便于讨论其性质,在几何外形设计、有限元分析及其它领域都有实用意义。文中给出具体的构造实例。 相似文献
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Leigh Tesfatsion 《Applied mathematics and computation》1980,6(1):51-61
In the absence of contrary information, it would seem prudent for competitors to attribute to their opposition the same level of rationality they attribute to themselves. In the context of a simple but interesting C3 (command, control, and communication) model presented in Ref. [3], a method is proposed for incorporating symmetrical rationality without resorting to the general multistage game framework which has proved difficult to apply in practice. A technique is suggested for the approximate solution of the resulting C3 model which does not require integration operations, and which appears to be especially well suited for C3 problems with finite admissible control sets. 相似文献
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Layne T. Watson 《Journal of Computational and Applied Mathematics》1979,5(2):131-139
S.N. Chow and J.A. Yorke have proposed in abstract terms an algorithm for computing fixed points of C2 maps that is globally convergent with probability one. A numerical implementation of that algorithm is presented here, where careful attention has been paid to computational efficiency, accuracy, and robustness. Convergence proofs for the numerical algorithm require differential geometry, and are given elsewhere. FORTRAN subroutines are given and explained in detail, and some typical numerical results are presented. It is shown how to modify the subroutines to compute zeros and handle some large sparse problems. 相似文献
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Chunhong FU 《数学年刊B辑(英文版)》2023,44(3):325-344
Motivated by two norm equations used to characterize the Friedrichs angle, this paper studies C*-isomorphisms associated with two projections by introducing the matched triple and the semi-harmonious pair of projections. A triple (P, Q, H) is said to be matched if H is a Hilbert C*-module, P and Q are projections on H such that their infimum P ∧ Q exists as an element of L(H), where L(H) denotes the set of all adjointable operators on H. The C*-subalgebras of L(H) generated by elements in {P - P ∧ Q, Q - P ∧ Q, I} and {P, Q, P ∧ Q, I} are denoted by i(P, Q, H) and o(P, Q, H), respectively. It is proved that each faithful representation (π, X) of o(P, Q, H) can induce a faithful representation (π, X e) of i(P, Q, H) such that e π(P - P ∧ Q) = π(P) - π(P) ∧ π(Q),eπ(Q - P ∧ Q) = π(Q) - π(P) ∧ π(Q).When (P, Q) is semi-harmonious, that is, R(P + Q) and R(2I - P - Q) are both orthogonally complemented in H, it is shown that i(P, Q, H) and i(I - Q, I - P, H) are unitarily equivalent via a unitary operator in L(H). A counterexample is constructed, which shows that the same may be not true when (P, Q) fails to be semi-harmonious. Likewise, a counterexample is constructed such that (P, Q) is semi-harmonious, whereas (P, I - Q) is not semi-harmonious. Some additional examples indicating new phenomena of adjointable operators acting on Hilbert C*-modules are also provided. 相似文献
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本文研究(Ⅱ)型三角剖分下带边界条件的二元二次样条插值问题的存在唯一性与插值节点分布的关系,并且在证明了中心插值、角点插值和偏心插值问题解的存在唯一性的基础上,给出了这三种插值函数的构造方法. 相似文献