共查询到17条相似文献,搜索用时 500 毫秒
1.
有理插值比多项式插值有更好的近似,但有理插值一般很难控制极点的产生.基于Thiele型连分式插值与重心有理插值,构造三元重心Thiele型混合有理插值,当选取适当的权后能避免部分极点的产生.文章最后通过数值例子验证了这种方法的正确性和有效性. 相似文献
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本文第一节利用 Samelson逆、混合偏差商以及 Thiele-型分叉连分式构造三元向量值混合有理插值 ,第二节给出了一种计算三元向量值混合有理插值的算法 ,第三节给出了一个数值例子 . 相似文献
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王家正 《应用数学与计算数学学报》2006,20(2):77-82
Stieltjes型分叉连分式在有理插值问题中有着重要的地位,它通过定义反差商和混合反差商构造给定结点上的二元有理函数,我们将Stieltjes型分叉连分式与二元多项式结合起来,构造Stieltje- Newton型有理插值函数,通过定义差商和混合反差商,建立递推算法,构造的Stieltjes-Newton型有理插值函数满足有理插值问题中所给的插值条件,并给出了插值的特征定理及其证明,最后给出的数值例子,验证了所给算法的有效性. 相似文献
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一般构造矩阵值有理函数的方法是利用连分式给出的,其算法的可行性不易预知,且计算量大.本文对于二元矩阵值有理插值的计算,通过引入多个参数,定义一对二元多项式:代数多项式和矩阵多项式,利用两多项式相等的充分必要条件通过求解线性方程组确定参数,并由此给出了矩阵值有理插值公式.该公式简单,具有广阔的应用前景. 相似文献
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1引言众所周知,有理插值是非线性逼近的一种重要方法,但由于其复杂性,主要表现在有理插值问题有解是有条件的或者说有理插值问题不是总是有解的.熟知的有理插值格式(包括向量有理插值、矩阵有理插值)函数构造方法,都是假定有理插值问题有解的条件下给出的,为实际应用带来一定的困难.目前,构造有理插值常用方法之一是基于连分式给出的,应用混合方法或分块方 相似文献
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关于Newton—Thiele型二元有理插值的存在性问题 总被引:1,自引:1,他引:0
基于均差的牛顿插值多项式可以递归地实现对待插值函数的多项式逼近,而Thiele型插值连分式可以构造给定节点上的有理函数。将两者结合可以得到Newton-Thiele型二元有理插值(NTRI)算法,本文解决了NTRI算法的存在性问题,并有数值例子加以说明。 相似文献
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一个二元矩阵插值连分式的展开式 总被引:2,自引:1,他引:1
本文借助于文[1]定义的一种实用的矩阵广义逆,构造了一个二元Stieltjes型矩阵值插值连分式的展开式,它的截断分式可以定义二元矩阵值插值函数. 相似文献
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詹棠森 《数学的实践与认识》2012,42(22):156-159
通过倒差商-连分式算法,提出了一种保端点非线性有理参数化拟合算法,通过选取中间点的参数化,利用连分式插值法,得到的拟合函数具有保端点性,规律性和灵活性.实例表明,算法减少了连分式插值迭代次数,避免插值连分式的不存在性,所得到拟合值具有更好的精度,大大提高了计算效率,拟合的误差更具有平稳性,逼近效果更好,并具有较好的预测等方面的应用. 相似文献
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Qianjin Zhao Jieqing Tan 《高等学校计算数学学报(英文版)》2007,16(1):63-73
This paper constructs a new kind of block based bivariate blending rational interpolation via symmetric branched continued fractions. The construction process may be outlined as follows. The first step is to divide the original set of support points into some subsets (blocks). Then construct each block by using symmetric branched continued fraction. Finally assemble these blocks by Newton’s method to shape the whole interpolation scheme. Our new method offers many flexible bivariate blending rational interpolation schemes which include the classical bivariate Newton’s polynomial interpolation and symmetric branched continued fraction interpolation as its special cases. The block based bivariate blending rational interpolation is in fact a kind of tradeoff between the purely linear interpolation and the purely nonlinear interpolation. Finally, numerical examples are given to show the effectiveness of the proposed method. 相似文献
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COMPUTATION OF VECTOR VALUED BLENDING RATIONAL INTERPOLANTS 总被引:3,自引:0,他引:3
檀结庆 《高等学校计算数学学报(英文版)》2003,12(1)
As we know, Newton's interpolation polynomial is based on divided differences which can be calculated recursively by the divided-difference scheme while Thiele 's interpolating continued fractions are geared towards determining a rational function which can also be calculated recursively by so-called inverse differences. In this paper, both Newton's interpolation polynomial and Thiele's interpolating continued fractions are incorporated to yield a kind of bivariate vector valued blending rational interpolants by means of the Samelson inverse. Blending differences are introduced to calculate the blending rational interpolants recursively, algorithm and matrix-valued case are discussed and a numerical example is given to illustrate the efficiency of the algorithm. 相似文献
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Newton-Thiele's rational interpolants 总被引:13,自引:0,他引:13
It is well known that Newton's interpolation polynomial is based on divided differences which produce useful intermediate
results and allow one to compute the polynomial recursively. Thiele's interpolating continued fraction is aimed at building
a rational function which interpolates the given support points. It is interesting to notice that Newton's interpolation polynomials
and Thiele's interpolating continued fractions can be incorporated in tensor‐product‐like manner to yield four kinds of bivariate
interpolation schemes. Among them are classical bivariate Newton's interpolation polynomials which are purely linear interpolants,
branched continued fractions which are purely nonlinear interpolants and have been studied by Chaffy, Cuyt and Verdonk, Kuchminska,
Siemaszko and many other authors, and Thiele-Newton's bivariate interpolating continued fractions which are investigated in
another paper by one of the authors. In this paper, emphasis is put on the study of Newton-Thiele's bivariate rational interpolants.
By introducing so‐called blending differences which look partially like divided differences and partially like inverse differences,
we give a recursive algorithm accompanied with a numerical example. Moreover, we bring out the error estimation and discuss
the limiting case.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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《分析论及其应用》2016,(1):65-77
General interpolation formulae for barycentric interpolation and barycentric rational Hermite interpolation are established by introducing multiple parameters,which include many kinds of barycentric interpolation and barycentric rational Hermite interpolation. We discussed the interpolation theorem, dual interpolation and special cases. Numerical example is given to show the effectiveness of the method. 相似文献
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二元混合连分式展开的混合差商极限方法 总被引:2,自引:0,他引:2
For a univariate function given by its Taylor series expansion,a continuedfraction expansion can be obtained with the Viscovatov's algorithm,as the limitingvalue of a Thiele interpolating continued fraction or by means of the determinantalformulas for inverse and reciprocal differences with coincident data points.In thispaper,both Viscovatov-like algorithms and Taylor-like expansions are incorporatedto yield bivariate blending continued expansions which are computed as the limitingvalue of bivariate blending rational interpolants,which are constructed based on sym-metric blending differences.Numerical examples are given to show the effectivenessof our methods. 相似文献
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Shuo Tang Yan Liang 《高等学校计算数学学报(英文版)》2007,16(3):271-288
Both the expansive Newton's interpolating polynomial and the Thiele-Werner's interpolation are used to construct a kind of bivariate blending Thiele-Werner's osculatory rational interpolation. A recursive algorithm and its characteristic properties are given. An error estimation is obtained and a numerical example is illustrated. 相似文献
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Newton's polynomial interpolation may be the favorite linear interpolation,associated continued fractions interpolation is a new type nonlinear interpolation.We use those two interpolation to construct a new kind of bivariate blending rational interpolants.Characteristic theorem is discussed.We give some new blending interpolation formulae. 相似文献