贯穿剖分上样条空间维数的注记

本文利用ｂｌｏｓｓｏｍ形式的光滑拼接条件，得到了贯穿剖分上样条空间维数定理的一个新的证明方法．     

加细剖分样条函数空间的维数级数和基函数

在文[1]中,我们讨论了利用协调矩阵计算维数级数和基函数的Grobner基方法,本文考虑几种加细剖分样条函数空间的维数级数和基函数,给出了它们的表达式。 1 任意三角剖分的连续样条函数 任意三角剖分上连续样条函数空间的维数早已被确定。本节我们用Grobner基方法来计算其维数级数的发生函数和基函数。 设Δ是单连通区域D上的三角剖分,f_0~0(Δ)是Δ内点的个数,f_1~0(Δ)是内网线的个数,f_2~0(Δ)是三角形的个数,我们有     

二元样条的积分表示及分层三角剖分下二次样条空间的维数

本文通过引入一个积分协调条件，首次给出了二元样条的一个积分表示．文中还定义了平面单连通多边形区域的所谓分层三角剖分，并确定了此剖分下二次样条空间的维数．     

Morgan-Scott剖分上样条空间S^48（△ms）的维数

Morgen-Scott剖分上样条空间的维数依赖于剖分的几何性质，本文证明了Diener 1990年提出的猜想对r=4是不正确的，需要修正．     

样条空间S~μ_k（△）的维数

本文考虑了欧式空间Ｒ￣ｎ中任意单纯形剖分上的样条函数空间．证明了当ｋ≥（３μ＋１）２￣（ｎ－２）＋１时，计算任意单纯形剖分Δ上的ｋ次μ阶光滑样条空间的维数，可归结为计算每个σ－关联域（ｉ－单纯形σ∈Δ）Ｒ（σ）上的２￣（ｎ－ｉ－１）μ次μ阶光滑（ｉ≤ｎ－１）样条空间的维数。这里σ－关联域Ｒ（σ）是指Δ中所有包含σ的单纯形所成的单纯形剖分．     

Morgan-Scott剖分上样条空间S_8~4(Δ_(ms))的维数

Ｍｏｒｇｅｎ－Ｓｃｏｔ剖分上样条空间的维数依赖于剖分的几何性质，本文证明了Ｄｉｅｎｅｒ１９９０年提出的猜想对ｒ＝４是不正确的，需要修正．     

多元弱样条函数空间的维数

讨论了多元弱样条一点处的维数公式及任意三角剖分下的维数公式．得到了１－型剖分下Ｗ_３^１（Ｉ₁Δ_ｍｎ^１）的维数与局部支集样条基．     

拟矩形剖分上的样条空间的维数

矩形剖分~(记为$\Delta_{QR}$)~是指在矩形剖分~(记为$\Delta_{R}$)的基础上进行局部修改后得到的剖分,通常包括T-剖分~(记为$\Delta_{T}$)~和L-剖分~(记为$\Delta_{L}$).本文利用光滑余因子协调方法讨论了该剖分上的二元样条空间$S^\mu_k(\Delta_{QR})$的维数.在满足一定约束条件下, 得到了仅依赖于样条空间的次数,光滑度和剖分拓扑结构的显式维数公式.     

一类分层三角剖分下三次样条空间的维数

本文定义了平面单连通多边形域的一类较任意的三角剖分－分层三角剖分，并通过分析二元样条的积分协调条件，确定了分层三角剖分卜三次Ｃ^１作条函数空间的维数．     

非均匀Ⅱ型三角剖分上的双周期三次样条函数空间

本文确立了非均匀Ⅱ型三角剖分上双周期三次样条函数空间的维数,并给出了一组具有局部支集的基底.     

Box－样条曲面的正性条件

研究了Ｂｏｘ－样条曲面的控制点与Ｂｏｘ－样条曲面的正性之间的关系．给出了Ｂｏｘ－样条曲面正性的必要条件、充分条件．由此我们得到了Ｂｏｘ－样条曲面的单调性条件，推广了Ｗ．ＤＡＨＭＥＮ和Ｃ．Ａ．ＭＩＣＣＨＥＬＬＩ在文［２］中给出的Ｂｏｘ－样条曲面的单调性结论     

Hilbertian Approach for Univariate Spline with Tension

In this work, a new approach is proposed for constructing splines with tension. The basic idea is in the use of distributions theory, which allows us to define suitable Hilbert spaces in which the tension spline minimizes some energy functional. Classical orthogonal conditions and characterizations of the spline in terms of a fundamental solution of a differential operator are provided. An explicit representation of the tension spline is given. The tension spline can be computed by solving a linear system. Some numerical examples are given to illustrate this approach.     

Hilbertian Approach for Univariate Spline with Tension

In this work, a new approach is proposed for constructing splines with tension. The basic idea is in the use of distributions theory, which allows us to define suitable Hilbert spaces in which the tension spline minimizes some energy functional. Classical orthogonal conditions and characterizations of the spline in terms of a fundamental solution of a differential operator are provided. An explicit representation of the tension spline is given. The tension spline can be computed by solving a linear system. Some numerical examples are given to illustrate this approach.     

Quintic nonpolynomial spline solutions for fourth order two-point boundary value problem

In this paper, we develop quintic nonpolynomial spline methods for the numerical solution of fourth order two-point boundary value problems. Using this spline function a few consistency relations are derived for computing approximations to the solution of the problem. The present approach gives better approximations and generalizes all the existing polynomial spline methods up to order four. This approach has less computational cost. Convergence analysis of these methods is discussed. Two numerical examples are included to illustrate the practical usefulness of our methods.     

HAZARD REGRESSION WITH PENALIZED SPLINE: THE SMOOTHING PARAMETER CHOICE AND ASYMPTOTICS

In this article, we use penalized spline to estimate the hazard function from a set of censored failure time data. A new approach to estimate the amount of smoothing is provided. Under regularity conditions we establish the consistency and the asymptotic normality of the penalized likelihood estimators. Numerical studies and an example are conducted to evaluate the performances of the new procedure.     

带参数的C~3连续拟Catmull-Rom样条函数

为了使得Catmull-Rom型样条兼具形状可调性与高阶连续性,提出了一类带参数的拟CatmullRom样条函数.该样条函数不仅无需求解方程系统即可自动达到C~3连续,而且还可通过所带的2个参数对插值曲线的形状进行调整·通过确定所带参数的最优取值,可获得最佳拟Catmull-Rom样条插值函数.     

Family of numerical methods based on non-polynomial splines for solution of contact problems

In this paper a new technique based on quartic non-polynomial spline functions connecting spline functions values at mid knots and their corresponding values of the fourth-order derivatives is developed. This approach leads to a family of numerical methods for computing approximations to the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. It is shown that the present family of methods gives better approximations. Existing second and fourth-order finite-difference and spline functions based methods developed at mid knots become special cases of the new approach. Numerical examples are given to illustrate applicability and efficiency of the new methods.     

On discrete hyperbolic tension splines

A hyperbolic tension spline is defined as the solution of a differential multipoint boundary value problem. A discrete hyperbolic tension spline is obtained using the difference analogues of differential operators; its computation does not require exponential functions, even if its continuous extension is still a spline of hyperbolic type. We consider the basic computational aspects and show the main features of this approach.     

关于三次样条插值矩阵非奇异的条件

在[1—4]中,讨论了三次插值样条存在唯一性亦即相应的插值矩阵非奇异的条件问题。本文则使用一个简单的技巧,导出插值矩阵非奇异的较简明的充要条件;由它可导出插值矩阵特征值分布的各种情形的特征性质;这一充要条件有简单的几何含义,因而容易得出插值矩阵非奇异的几个充分条件。它使[4]的结果更为直观,并得到改     

W_2~m空间中样条插值算子与线性泛函的最佳逼近

In this paper,the convergency of spline interpolation operators is obtained,these spline operators are determined by linear differential operators and constraint functionals.The errors of the interpolating spline with EHB fanctionals are estimated.The best approximation of linear functionals on W2^n spaces are investigated,which let to a useful computational method for the approximation solution of higher order linear differential equations with multipoint boundary value conditions.