排序方式: 共有6条查询结果,搜索用时 0 毫秒
1
1.
2.
本文论述(2n+1)次样条函数的一种构造方法。此法规律简单,计算方便。每当次数增高两次时,只需在原来的样条函数上增加两项就能得到,并且由这种样条本身的性质得到了一个简单的判断曲线凹凸性的充分条件。 相似文献
3.
4.
由[1]中调配函数的性质3及5可知,当j为奇数时,f_(2j 1)(t)及g_(2j 1)(t)都是[0,1]上点(0,0)及点(1,0)之间的一段凹弧;当j为偶数时,为此二点间的一段凸弧. 下面仅就g_(2j 1)(t)来讨论.如上所述,可知g_(2j 1)(t)在[0,1]上是单调函数,且g_(2j 1)(0)与g_(2j 1)(1)异号,即 相似文献
5.
熊振翔 《应用数学与计算数学学报》1988,(2)
县1.函数在两点的插值多项式及其导数的余项满足条件P盆乏己,:(a‘)二F(”,)(a‘),i二o,1;j二o,1,2,…,n一1}一均多月!人(1 .1)其中h=al一a。,v二一1(x)二艺〔F(“,)(a。)f:,+1(v)+F(“’)(a,)夕:,一卜1(v)]hZ’, 7二0兰二粤,xc〔a。,。1],称为尸(二)在两点a。及a,的(2。一‘) h’一’~‘一“’一二J”‘’/J‘、一z‘一’“、、一“人“一火卜“、一”次插值多项式.这里f:,*:(。)及夕:,十,(v)是Zj+1次多项式,它们的定义及系数的算法见〔2〕及〔3〕. 定理1设F(x)任CZ“〔a。,al〕,则存在雪〔(a。,al),使得F(二)=艺[F(2’)(a。)f:,十1(… 相似文献
6.
The multivariate splines which were first presented by deBooor as a complete theoreticalsystem have intrigued many mathematicians who have devoted many works in this field whichis still in the process of development.The author of this paper is interested in the area of inter-polation with special emphasis on the interpolation methods and their approximation orders.But such B-splines(both univariate and multivariate)do not interpolated directly,so I ap-proached this problem in another way which is to extend my interpolating spline of degree2n-1 in univariate case(See[7])to multivariate case.I selected triangulated region which isinspired by other mathematicians'works(e.g.[2]and[3])and extend the interpolatingpolynomials from univariate to m-variate case(See[10])In this paper some results in thecase m=2 are discussed and proved in more concrete details.Based on these polynomials,theinterpolating splines(it is defined by me as piecewise polynomials in which the unknown par-tial derivatives are determined under certain continuous conditions)are also discussed.Theapproximation orders of interpolating polynomials and of cubic interpolating splines areinverstigated.We lunited our discussion on the rectangular domain which is partitioned intoequal right triangles.As to the case in which the rectangular domain is partitioned into unequalright triangles as well as the case of more complicated domains,we will discuss in the next pa-per. 相似文献
1