第三章研究了一元切触有理插值的存在性。
The chapter 3, we study the existence of univariate osculator rational interpolants.
以二元向量有理插值为基础，提出了一种新的图像缩放方法。
对所构造的切触有理插值函数，还可通过选择参数降低其次数。
For osculatory rational interpolating function that we have constructed, we can reduce its number of times by choosing parameters.
采用重心有理插值近似未知函数，得到未知函数的各阶微分矩阵。
The differentiation matrices of unknown function are constructed by using barycentric rational interpolation.
已有的构造切触有理插值函数方法，多数是与连分式计算相联系的。
Existing methods of constructing oscillatory rational interpolating function are almost related to calculation of continued fractions.
然后构造了在预给极点情况下求主对角线和副对角线上向量值有理插值的矩阵算法。
In addition this paper constructs a matrix algorithm for computing bivariate diagonal vector valued rational interpolants with preassigned poles.
本文将在切触有理插值中起重要作用的Salzer定理推广到了多元向量的情形。
In this paper, the important Salzer's theorem for rational interpolation is generalized to the multivariate vector valued case.
第四章主要讨论了二元向量有理插值的迭加算法及二元向量切触有理插值的表现公式。
The chapter 4, we mainly discuss the overlay algorithm of two-variable vector-valued rational interpolation and show formula of two-variable vector-valued contact interpolation.
受二元多项式插值的迭加算法的启发，给出一种简便的求有理插值函数的方法，同时通过实例进行验证。
Enlighened by the superposed algorithm of two element polynomial interpolation, we present a simple method of finding rational interpolation functions.
本文给出了关于有理插值正则解的充要条件的一个定理，其证明是简单的，作为判别法则使用亦是方便的。
This paper puts forward the theorem dealing with the necessary and sufficient condition of the regular solution to the rational interpolation. The theorem is simple to prove and convenient to use.
把四次有理插值样条函数的连续性降为C2连续就可以提供额外的自由度，这对于控制曲线的形状具有较大的灵活性。
If we decrease the splines continuity to C2 continuous, it can provide additional freedom degree, and this is very useful for shape constraint in curve design.
利用构造出的多边形有理插值，采用凸多边形逼近任意凸域，通过区域边界温度离散值，插值近似区域内的温度场分布。
A convex domain is approached by a convex polygon, and the approximated temperature distribution within the domain can be interpolated with the temperature data at the boundaries of the domain.
然后利用插值型值点复数化的方法及向量值连分式的向后三项递推关系式讨论并给出了二元向量值有理插值的一种新算法。
Then a new algorithm of brivate vector -valued rational interpolants by means of complexification of the knots and backward three-term recurrence relations is given.
采用几何的方法构造出多边形单元上的有理函数插值。
Adopting geometric method, the rational function interpolation is constructed on polygonal element.
讨论了一类插值有理函数对可微函数的逼近，得到了相应的逼近阶。
The approximation of differentiable functions by a kind of interpolatory rational functions is discussed, and the corresponding order of approximation is obtained.
给出了具有线性分母的有理三次样条函数的误差估计，并在柱面坐标系下对一类空间闭曲线的插值问题进行了研究；
The error estimation of rational cubic spline with linear denominators is given, and then the interpolation of a kind of space closed curves under cylindrical coordinate system is investigated.
借鉴自然邻点插值法，提出了基于高度不规则网格多边形单元的有理函数插值格式—多边形有理函数插值。
This paper presents a rational function interpolation scheme of polygonal elements based on highly irregular grids. It is named as polygonal rational function interpolation (RFI).
因此，本文提出的自适应有理函数插值方法可以对大量采样数据进行插值运算而不会遇到奇异性问题。
So the adaptive rational function interpolation method can process a large number of sampling data for obtaining a rational interpolation without suffering singularity problems.
本课题对有理函数插值方法的理论及其算法进行了研究。
This paper discusses the theory and several algorithms of rational function interpolation.
这一特性使得AFS方法能通过简单的有理函数实现宽带插值。
This attribute virtually leads the proposed AFS approach to an ultra broad-band interpolation with a single rational function.
本文提出了一个在三角形域上的有理布尔和插值的新方法，此方法的特点是所构造的插值函数结构简单，多项式准确集较高。
A new method of rational Boolean sum interpolation on an arbitrary triangle is developed in this paper. The structure of the interpolation function is simple.
首先将有理函数阻抗矩阵插值技术应用于采用预条件器加速的矩量法求解过程。
Firstly, impedance matrix interpolation is incorporated in MoM in combination with the preconditioning technique.
给出一种简单的有理分式插值——差分样条插值。
In this paper we give a simple interpolation of rational function-difference spline interpolation.
给出一种简单的有理分式插值——差分样条插值。
In this paper we give a simple interpolation of rational function-difference spline interpolation.
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