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1.
Algorithms are presented for the construction of histopolating splines consisting of linear/linear rational or quadratic polynomial pieces. A unique comonotone histospline of such kind exists for any histogram with weak alternation of data. In general case, without weak alternation of data, a modified comonotone spline histopolation strategy should be used. The method is implemented via the representation with histogram heights and knot values of first derivatives of the spline. Numerical examples are given. 相似文献
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《Journal of Computational and Applied Mathematics》2005,175(2):195-208
For given monotone data we propose the construction of a histopolating linear/linear rational spline of class C1. The uniqueness and existence of this spline is proved. The method is implemented via the representation with histogram heights and first derivatives of the spline. The use of Newton's method and ordinary iterations are discussed. Numerical tests support completely the theoretical results. 相似文献
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In order to relieve the deficiency of the usual cubic Hermite spline curves, the quartic Hermite spline curves with shape parameters is further studied in this work. The interpolation error and estimator of the quartic Hermite spline curves are given. And the characteristics of the quartic Hermite spline curves are discussed. The quartic Hermite spline curves not only have the same interpolation and conti-nuity properties of the usual cubic Hermite spline curves, but also can achieve local or global shape adjustment and C2 continuity by the shape parameters when the interpolation conditions are fixed. 相似文献
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基于一类与给定多边形相切的三角样条曲线,通过在基函数中引入形状参数λ,在保持原曲线的光滑性及其他基本性质不变的条件下,构造出一类能自由调控曲线形态的含参数三角样条曲线,并结合图例讨论了其相关性质. 相似文献
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A class of spline curves with four local shape parameters, which includes the quartic spline curves with three local shape parameters given in Han [Xuli Han. A class of general quartic spline curves with shape parameters. Comput. Aided Geom. Design, 28: 151–163 (2011)], is proposed. Without solving a linear system, the spline curves can be used to interpolate sets of points with C2 continuity partly or entirely. The shape parameters have a predictable adjusting role on the spline curves. 相似文献
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This paper is concerned with numerical methods in range restricted histopolation. The proposal is to apply splines on refined
grids. The ratios of the added split points are considered to be parameters. In this way, by choosing suitable spline classes,
range restricted histosplines can always be constructed if the restrictions are compatible with the given histogram. We offer
an algorithm for solving the bivariate problem on a rectangular grid which utilizes univariate results as well as tensor product
techniques.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
8.
We propose a new method to approximate a given set of ordered data points by a spatial circular spline curve. At first an initial circular spline curve is generated by biarc interpolation. Then an evolution process based on a least-squares approximation is applied to the curve. During the evolution process, the circular spline curve converges dynamically to a stable shape. Our method does not need any tangent information. During the evolution process, the number of arcs is automatically adapted to the data such that the final curve contains as few arc arcs as possible. We prove that the evolution process is equivalent to a Gauss-Newton-type method. 相似文献
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We study the reconstruction of a function defined on the real line from given, possibly noisy, data values and given shape constraints. Based on two abstract minimization problems characterization results are given for interpolation and approximation (in the euclidean norm) under monotonicity constraints. We derive from these results Newton-type algorithms for the computation of the monotone spline approximant. 相似文献
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为了更好地修改给定的样条曲线曲面,构造了满足几何连续的带两类形状参数的代数三角多项式样条曲线曲面,简称为AT-β-Spline.这种代数三角曲线曲面不仅具有普通三角多项式的性质,而且具有全局的和局部的形状可调性.同时还具备较为灵活的连续性.当两类形状参数在给定的范围内任意取值时,这种带两类形状参数的AT-β-Spline曲线满足一阶几何连续性;如果给定两段相邻曲线段中的两类形状参数满足-1≤α≤1,μ_i=λ_(i+1)或μ_i=λ_i=μ_(i+1)=λ_(i+1)时,则带两类形状参数的AT-β-Spline曲线满足C~1∩G~2连续.另外利用奇异混合的思想,构造了满足C~1∩G~2插值AT-β-Spline曲线,解决曲线反求的几何连续性等问题.同时还给出了旋转面的构造,描述了两类形状参数对旋转面的几何外形的影响;当形状参数取特殊值时,这种AT-β-Spline曲线曲面可以精确地表示圆锥曲线曲面.从实验的结果来看,本文构造的AT-β-Spline曲线曲面是实用的有效的. 相似文献
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A Review of Some Non-parametric Methods of Density Estimation 总被引:1,自引:0,他引:1
This paper lists and reviews most of the many papers publishedon the subject of density estimation. The four main categoriesof estimators (kernel, spline, orthogonal series and histogram)are compared not only for their theoretical properties but alsofor their applicability to real life problems. 相似文献
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Prabir Burman 《Probability Theory and Related Fields》1985,69(4):609-628
Summary A data dependent approach to density estimation is proposed here. The proposed method requires boundedness and some weak integrability condition on the unknown density, but not any assumption of smoothness. Applications to histogram, kernel, spline and orthogonal series methods are discussed. 相似文献
16.
We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal spline estimators for regression, density estimation, and arrival rate estimation problems in the presence of various shape constraints. Our approach can also handle multiple simultaneous shape constraints. The approach is based on a characterization of nonnegative polynomials that leads to semidefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problems. These formulations extend and generalize a number of previous approaches in the literature, including those with piecewise linear and B-spline estimators. We also consider a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis. A condition is presented to test whether a given nonnegative basis gives rise to a spline cone that is dense in the space of nonnegative continuous functions. The optimization models formulated in the article are solvable with minimal running time using off-the-shelf software. We provide numerical illustrations for density estimation and regression problems. These examples show that the proposed approach requires minimal computational time, and that the estimators obtained using our approach often match and frequently outperform kernel methods and spline smoothing without shape constraints. Supplementary materials for this article are provided online. 相似文献
17.
C^3连续的保形插值三角样本曲线 总被引:2,自引:0,他引:2
本给出了构造保形插值曲线的三角样条方法,即在每两个型值点之间构造两段三次参数三角样条曲线。所构造的插值曲线是局部的,保形的和C^3连续的而且曲线的形状可由参数调节。 相似文献
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在实际问题中,尤其是统计问题,碰到的不一定是点态插值,而是要满足某种平均泛函条件.本文讨论算子样条积分平均插值,给出一种新的、计算稳定的求解算法. 相似文献
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Vladimir K. Kaishev Dimitrina S. Dimitrova Steven Haberman Richard J. Verrall 《Computational Statistics》2016,31(3):1079-1105
A new method of Geometrically Designed least squares (LS) splines with variable knots, named GeDS, is proposed. It is based on the property that the spline regression function, viewed as a parametric curve, has a control polygon and, due to the shape preserving and convex hull properties, it closely follows the shape of this control polygon. The latter has vertices whose x-coordinates are certain knot averages and whose y-coordinates are the regression coefficients. Thus, manipulation of the position of the control polygon may be interpreted as estimation of the spline curve knots and coefficients. These geometric ideas are implemented in the two stages of the GeDS estimation method. In stage A, a linear LS spline fit to the data is constructed, and viewed as the initial position of the control polygon of a higher order (\(n>2\)) smooth spline curve. In stage B, the optimal set of knots of this higher order spline curve is found, so that its control polygon is as close to the initial polygon of stage A as possible and finally, the LS estimates of the regression coefficients of this curve are found. The GeDS method produces simultaneously linear, quadratic, cubic (and possibly higher order) spline fits with one and the same number of B-spline coefficients. Numerical examples are provided and further supplemental materials are available online. 相似文献