多层积分值三次样条拟插值

目的 在实际问题中,某些插值问题结点处的函数值往往是未知的,而仅仅知道一些连续等距区间上的积分值。为此提出了一种基于未知函数在连续等距区间上的积分值和多层样条拟插值技术来解决函数重构。该方法称之为多层积分值三次样条拟插值方法。方法 首先,利用积分值的线性组合来逼近结点处的函数值;然后,利用传统的三次B-样条拟插值和相应的误差函数来实现多层三次样条拟插值;最后,给出两层积分值三次样条拟插值算子的多项式再生性和误差估计。结果 选取无穷次可微函数对多层积分值三次样条拟插值方法和已有的积分值三次样条拟插值方法进行对比分析。数值实验印证了本文方法在逼近误差和数值收敛阶均稍占优。结论本文多层三次样条拟插值函数能够在整体上很好的逼近原始函数,一阶和二阶导函数。本文方法较之于已有的积分值三次样条拟插值方法具有更好的逼近误差和数值收敛阶。该方法对连续等距区间上积分值的函数重构具有普适性。     

逼近三次B 样条导矢曲线的四次Hermite 插值样条

给出了形状可调的四次Hermite 插值样条曲线的构造方法。四次样条曲线可提供额 外的自由度用于调整曲线具有合理形状。利用导矢逼近使得四次Hermite 样条曲线具有与三次B 样条曲线相似的形状。通过最小化曲线间的导矢误差给出了确定自由度的方法,提出了四次 Hermite 插值样条曲线的构造方法。该方法增加了自由度控制曲线形状能更好满足保形要求。最 后以实例对构造的四次Hermite 样条曲线和标准三次Hermite 插值样条曲线进行了比较。     

基于张力格林样条的EMD均值曲线插值方法

经典经验模式分解采用三次样条插值方法求取信号的均值曲线,其存在较严重的过冲现象,造成最终的分解误差较大。针对上述问题,提出一种基于张力格林样条的均值曲线插值方法。以相邻极值点的中点为插值节点,采用张力格林样条插值直接获得信号的均值曲线。实验结果表明,该方法在保证插值曲线光滑性的基础上,可以消除三次样条在插值节点间出现的过分振荡现象,一定程度上克服过冲问题,基于极值中点的一次插值能进一步降低信号分解的误差。     

基于三次样条插值的硅压阻式压力传感器的温度补偿

传感器的零点温度漂移、灵敏度温度漂移和非线性误差是影响传感器性能的主要因素,如何能使该类误差得到有效补偿对于提高其性能有重要意义。提出了基于三次样条曲线插值的温度补偿方法,改进了传统三次样条曲线插值的补偿方法,分别对传感器的零点、灵敏度以及非线性进行补偿,用这种方法对测压范围为1.0140×105 Pa～3.0140×105 Pa,温度范围为-20℃～+60℃的硅压阻式压力传感器的实验标定结果进行了温度补偿。通过比较传统三次样条插值补偿后的传感器输出信号,验证了使用改进后的三次样条曲线插值法的补偿效果更好。这种方法为高精度压力传感器的温度补偿提供了一种有价值的理论依据。     

三次Cardinal样条函数的自由参数优化方案

为了合理地取定三次Cardinal样条函数所含的自由参数,讨论了插值问题中三次Cardinal样条函数所含自由参数的优化问题。首先分析了自由参数对三次Cardinal样条函数曲线形状的影响,然后给出了数据插值与函数逼近这2种情形下自由参数最优取值的计算方案,分别得到了具有极小二次平均振荡与极小逼近误差的三次Cardinal样条函数。当需要构造具有良好形状保持效果或逼近效果的三次Cardinal样条函数时,可通过所提出的方案选取自由参数的最优取值。     

有理三次样条的误差分析及空间闭曲线插值

给出了具有线性分母的有理三次样条函数的误差估计,并在柱面坐标系下对一类空间闭曲线的插值问题进行了研究;通过将柱面展开,把空间闭曲线的插值问题转化为平面中的插值问题,利用具有线性分母的有理三次样条函数进行插值;最终得到的空间曲线能达到曲率连续.对该方法的误差进行了分析,数值例子显示插值效果较好.     

关于三次样条插值方法在应用中的一点改进

本文简要介绍了对三次样条函数插值方法在某些特殊应用中的一点改进意见,通过改进,使三次样条函数插值方法具有了更广泛的适用性。     

二维二次样条及其化工应用

推导了二维二次多项式样条系数的计算公式与步骤,又用经作者扩充到二维情况的Runge函数作为基准对二维二次样条和Lagrange插值通过误差对比说明了样条的优点。本文还考察了将二维二次样条用于逼近各类典型的二维化工曲线族的误差,发现只要选取恰当的起始点和合适的节点布置,一般均能获得满意的精度。     

NURBS曲线相关积分量的计算方法

本文给出了求２次和３次非均匀有理Ｂ样条（ＮＵＲＢＳ）曲线的相关积分量，例如它所包围区域的面积、旋转体体积、面积矩、形心等的算法．对于２次曲线，本文推导了一系列精确的积分公式，由此，所有积分量可用曲线的控制顶点坐标和权因子一步代入直接求得而没有逼近误差；对于３次曲线，本文展示了一种近似算法，与通常的数值积分法相比，它具有误差界估计简单，高精度下收敛速度快等优点．     

一种基于三次样条函数求离子浓度的自动算法

本文提出了一种用三次样条函数模拟双次标准加入法测量方程，直接求解离子浓度的自动算法。比较了三咱不同边界条件下用要池数计算离子浓度的结果。造出节点区间两极端点的二阶导数为零时的三次样条函数为最佳模拟函数。并讨论了该方法在实际分析中误差的来源及消除办法。经对一系列文献数据的验算对比，表明本法完全可代替传统的迭代法和查图法，且能方便地设置在智能化的电位分析系统中。     

Optimizing at the end-points the Akima's interpolation method of smooth curve fitting

In this paper we propose an optimized version, at the end-points, of the Akima's interpolation method for experimental data fitting. Comparing with the Akima's procedure, the error estimate, in terms of the modulus of continuity, is improved. Similarly, we optimize at the end points the Catmull–Rom's cubic spline. The properties of the obtained splines are illustrated on a numerical experiment.     

Sampling of signals and their reconstruction

This paper gives error bounds when a stochastic process or a deterministic signal is sampled and reconstruction is done either by piecewise straight lines or cubic splines. In the case of cubic splines the error bounds derived here take into account the number of samples. Using the results presented here it is possible to select the sampling interval for a given error.     

Non-polynomial splines method for numerical solutions of the regularized long wave equation

In this paper, we construct a numerical method based on cubic splines in tension for solving regularized long wave equation. The truncation error is analysed and the method shows that by choosing suitably parameters we can obtain various accuracy schemes. Numerical stability of the method has been studied by using a linearized stability analysis. Test problems are dealt with. The numerical simulations can validate and demonstrate the advantages of the method.     

Algorithm/algorithmus 42 an algorithm for cubic spline fitting with convexity constraints

In this paper an algorithm is presented for fitting a cubic spline satisfying certain local concavity and convexity constraints, to a given set of data points. When using theL ₂ norm, this problem results in a quadratic programming problem which is solved by means of the Theil-Van de Panne procedure. The algorithm makes use of the well-conditioned B-splines to represent the cubic splines. The knots are located automatically, as a function of a given upper limit for the sum of squared residuals. A Fortran IV implementation is given.     

带参数的四次Hermite插值样条

为了克服标准三次Hermite插值样条的不足,给出了一种带参数的四次Hermite插值样条,具有标准三次Hermite插值样条完全相同的性质。在插值条件给定时,四次Hermite插值样条的形状可通过改变参数的取值进行调控。通过选择合适的参数,四次Hermite曲线能达到C2连续,而且其整体逼近效果要好于标准三次Hermite插值样条。所提出的新样条进一步丰富了Hermite插值样条理论,也为工程中插值曲线曲面的构造提供了一种新方法。     

三次样条构造的伪逆解法

为了提高三次样条构造的可行性, 基于矩阵的伪逆方法, 提出一种不依赖额外约束条件的三次样条构造的伪逆解法。该解法通过求解出三次样条二阶导数的最小范数解, 从而较好地构造出三次样条函数。理论分析及数值实验结果表明该三次样条构造的伪逆解法具有简单、有效等特点。综合分析各种构造解法的性质, 对各种三次样条构造解法进行归类比较, 为在实际工程计算应用中选择合适的三次样条构造解法提供了指导方向。     

Un metodo per la costruzione di smoothing splines con la programmazione lineare

A method for the construction of cubic smoothing splines is studied by optimizing the curvature of this function. The main tool is the linear programming. In this way the property of minimal curvature of cubic natural splines is improved and generalized. A numerical example is shown.      

Multidimensional Spline Interpolation: Theory and Applications

Computing numerical solutions of household’s optimization, one often faces the problem of interpolating functions. As linear interpolation is not very good in fitting functions, various alternatives like polynomial interpolation, Chebyshev polynomials or splines were introduced. Cubic splines are much more flexible than polynomials, since the former are only twice continuously differentiable on the interpolation interval. In this paper, we present a fast algorithm for cubic spline interpolation, which is based on the precondition of equidistant interpolation nodes. Our approach is faster and easier to implement than the often applied B-Spline approach. Furthermore, we will show how to loosen the precondition of equidistant points with strictly monotone, continuous one-to-one mappings. Finally, we present a straightforward generalization to multidimensional cubic spline interpolation.