关于非等距的五次样条函数的缺插值

一f(x)是区间[0,1]上定义的函数,0=x_0相似文献   

用样条函数的缺插值(Ⅱ)

f(x)是区间[0,1]上定义的函数,n是奇数,把[0,1]n等分,记 h=1/n,f~((r))(vh)=f_v~((r)),v=0,1,…,n;r=0,1,2,3.A.Meir和 A,Sharma,B.K.Swartz和 R.S.Varga及作者考虑了五次缺插     

用样条函数的缺插值

<正> f(x)是区间[0,1]上定义的函数,n 是奇数,把[0,1]n 等分,记h=1/n,f~(r)(vh)=f_v~(r),v=0,1,…,n;r=0,1,…,5.A.Meir 和 A.Sharma 提出五次缺插值样条函数,即满足下面条件的五次样条函数 S_n(x):     

具有共振的边值问题解的存在性

利用Mawhin的重合度理论,研究具有共振的n-阶m-点边值问题x~((n))(t)=f(t,x(t),x′(t),…,x~((n-1))(t)),t∈(0,1)x(0)=x(η),x′(0)=x″(0)=…=x~((n-2))(0)=0,x~((n-1))(1)=α_ix~((n-1))(ξ_i)解的存在性,其中n≥2,m≥3,f:[0,1]×R~n→R将有界集映为有界集,且当x(t)∈C~(n-1)[0,1]时,f(t,x(t),x′(t),…,x~((n-1))(t))∈L~1[0,1],0<ξ_1<ξ_2<…<ξ_(m-2)<1,0<η<1,α_i∈R.在这里并不要求f具有连续性.     

用样条函数缺插值的一点注记

(ii)在区间[vh,(v 1)h]上S_n(x)是五次多项式,v= 0,1…,n-1;(1) (iii)S_n(vh)=f_v,S″_n(vh)=f″_v,v=0.1,…,n的五次样条函数S_n(x)存在且唯一.我们依次得到下列的逼近定理:     

二次插值样条导数误差的准确界

[1]和[2]分别解决了三次插值样条的二阶和三阶导数的最优误差界。由于二次样条也同样广泛地被讨论和应用,因此作出其最优误差估计也有理论和实际意义。 设△_n是[0,1]的一个均匀分划:0=x_0<…相似文献   

三次样条函数的渐近展开和超收敛性

<正> 对[0,1]上的等距分划0=x_0相似文献   

五次缺插值样条的渐近性态

f(x)定义于[0,1]。将[0,1]n等分,记x_j=jh,j=0,…,n.h=1/n,且 f~(α)(x_j)=f_j~(α),j=0,…,n;α=0,1,…,5。 A.Meir和A.Sharma提出五次缺插值样条函数,即满足下面条件的函数s_n(x): (i)s_n(x)∈C~3[0,1], (ii)在区间[x_j,x_(j 1)]上(j=0,…,n-1),s_n(x)是五次多项式, (iii)s_n(x_j)=f_j,s″_n(x_j)=f″_j,j=0,…,n, (iv)s′_n(0)=f′_0,s′_n(1)=f′_n。 (1) [1]还考虑了把(1)中的(iv)换成 (iv′)s′′′_n(0)=f′′′_0,s′′′_n(1)=f′′′_n (2)的五次样条。为叙述方便,我们分别称之为(Ⅰ)型、(Ⅱ)型缺插值样条。[1]证明了(Ⅰ),(Ⅱ)型插值样条在n为奇数时是唯一存在的。[2,3,4]继续了这方面的工作,得到了一     

用样条函数描述函数构造性质

本文通过插值样条函数研究函数的构造性质。设f(x)∈L_p[0,1],S_n(f;x)为其插值样条函数。文中给出用‖S_n~((r))(f;x)‖_p来描述f~((r))(x)∈L_p[0,1]的充要条件。对于相当一类的插值样条和缺插值样条文中的结果均能适用。     

关于(o,M)型缺三角插值多项式的同等收敛性

本文将给出有关(0,M)型缺三角掐值多项式的同等收敛性定理。设f(x)∈C_(2x),Q_n(f,x)为满足下述条件且在x_(kn)处插值于f(x)的(0,M)型缺三角插值多项式:Q_n(f,X_(kn)=f(X_(kn)),Q_n~((M))(f,X_(kn))=0,这里X_(kn)=(2kx/n),n=2m+1,k=0,1,…,n—1。由文[3]中的结论,这样的Q_n(f,x)存在且唯一。     

Depth notions for orthogonal regression

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.     

Periodic and solitary-wave solutions of the Degasperis–Procesi equation

Travelling-wave solutions of the Degasperis–Procesi equation are investigated. The solutions are characterized by two parameters. For propagation in the positive x-direction, hump-like, inverted loop-like and coshoidal periodic-wave solutions are found; hump-like, inverted loop-like and peakon solitary-wave solutions are obtained as well. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. A transformed version of the Degasperis–Procesi equation, which is a generalization of the Vakhnenko equation, is also considered. For propagation in the positive x-direction, hump-like, loop-like, inverted loop-like, bell-like and coshoidal periodic-wave solutions are found; loop-like, inverted loop-like and kink-like solitary-wave solutions are obtained as well. For propagation in the negative x-direction, well-like and inverted coshoidal periodic-wave solutions are found; well-like and inverted peakon solitary-wave solutions are obtained as well. In an appropriate limit, the previously known solutions of the Vakhnenko equation are recovered.     

State models and asymptotic behaviour of 2D positive systems

Homogeneous 2D positive systems are 2D state-space models whosevariables are alwalys nonnegative and, consequently, are describedby a pair of nonnegative square matrices (A, B). In the paper,the properties of these pairs are discussed both in the generalcase and under particular assumptions like finite memory, separability,and property L. Various aspects of the positive asymptotic dynamic are considered;in particular, sufficient conditions are provided guaranteeingthat the local states are eventually strictly positive. Finally,some results on the convergence of the states towards a constantasymptotic distribution are presented.     

MTL代数的特征定理

对于逻辑系统代数结构的研究,是一个十分重要的研究课题.近期提出的BL代数,R_0代数,MTL代数就是这个方向具有代表性的研究成果.本文讨论MTL代数的性质与结构,给出这种代数的几个特征定理,澄清这种代数与其它代数结构的关系.鉴于单位区间中由左连续t-范数诱导的剩余蕴涵与MTL代数的紧密联系,本文还考察了这种模糊蕴涵的特征性质.     

近程空中目标航路研究

本文在等加速俯冲飞行假定下，分析了近程空中目标航路的特点，并据此提出了目标航路模型．经过投影变换，把目标航路模型转化为二次函数，从而使目标航路的滤波及预报问题得到简化．采用递推最小二乘（ＲＬＳ）原理，给出了目标航路的在线滤波器及预报器．最后，对本文方法进行了仿真，并对仿真结果进行了分析．     

秩为1矩阵的性质及应用

给出了秩1矩阵的结构,讨论了这类矩阵在矩阵运算、对角化、标准型等方面的性质,推广和改进了文[1]的一些相关结果,并指出了它的若干应用,重点讨论了一类矩阵,得到了有关结论和方法.     

Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof. Lu Jianke

In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.     

On the boundedness and unboundedness of external polyhedral estimates for reachable sets of linear differential systems

The boundedness and unboundedness properties of external polyhedral (paralle-lepiped-valued) estimates are investigated for reachable sets of linear differential systems with a stable matrix. Boundedness and unboundedness criteria on an infinite time interval are presented for two types of estimates (“touching” estimates, which were introduced earlier, and estimates with constant orientation matrix). Conditions for the system matrix and bounding sets are given under which there are bounded estimates among the estimates of the mentioned types, under which there are unbounded estimates, and under which all the estimates are bounded or all the estimates are unbounded. In terms of the exponents of the estimates, the possible rate of their growth is described. For two-dimensional systems, the classification and comparison of possible situations of the boundedness or unboundedness for estimates of both types are given and boundedness criteria for estimates with special (orthogonal and “quasi-orthogonal”) constant orientation matrices are found. Results of numerical modeling are presented.     

Some properties of singular integral operators over an open curve Dedicated to the 85th birthday of Prof.Lu Jinake

In this paper, the stability properties, the endpoint behavior and the invertible relations of Cauchy-type singular integral operators over an open curve are discussed. If the endpoints of the curve are not special, this type of operators are proved to be stable. At the endpoints, either the singularity or smoothness of the operators are exactly described. And the function sets or spaces on which the operators are invertible as well as the corresponding inverted operators are given. Meanwhile, some applications for the solution of Cauchy-type singular integral equations are illustrated.