关于Thiele型向量值连分式收敛定理的一个注记

本文利用推广的向量连分式向后递推算法重新给出了文[3]中定理1的证明,并改进了其结果。最后,在稍强的条件下,给出了这一类收敛向量连分式的一个更精致的截断误差估计。     

基于二元连分式的散乱数据递推插值格式

本文首先基于新的非张量积型偏逆差商递推算法,分别构造奇数与偶数个插值节点上的二元连分式散乱数据插值格式,进而得到被插函数与二元连分式间的恒等式.接着,利用连分式三项递推关系式,提出特征定理来研究插值连分式的分子分母次数.然后,数值算例表明新的递推格式可行有效,同时,通过比较二元Thiele型插值连分式的分子分母次数,发现新的二元插值连分式的分子分母次数较低,这主要归功于节省了冗余的插值节点. 最后,计算此有理函数插值所需要的四则运算次数少于计算径向基函数插值.     

Perturbed Recurrence Relations

In this paper, we give some new relations between two families of polynomials defined by three-term recurrence relations. These relations allow us to study how some properties of a family of orthogonal polynomials are affected when the coefficients of the recurrence relation are perturbed. In the literature some methods are already available. However, most of them are only effective for small perturbations. In order to show the sharpness of our method, we compare it with Gronwall's classical method in the case of large perturbations. Using our tool, we also give a relation between the differential equation satisfied by a family of orthogonal polynomials and its perturbed family. Some explicit results are obtained for Chebyshev polynomials of the second kind.     

The Levels-Recursive Algorithm for Vector Valued Interpolants by Triple Branched Continued Fractions

1 Introduction Let Πl,m,n be a set of points in three dimensional space R3, Πl,m,n = {(xi, yj, zk), i = 0, 1, · · · l; j = 0, 1, · · · m; k = 0, 1, · · · n}. Let a d?dimensional vector vi,j,k be given at every point (xi, yj, zk) ∈ Πl,m,n and     

On Sufficient Conditions for Convergence of Two-Dimensional Continued Fractions

By the method of majorant fractions and equivalent transformations, the analogies of leszyski–Pringsheim criteria for two-dimensional continued fractions are obtained.     

一个二元矩阵插值连分式的展开式

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.     

Continued Fractions and Unique Additive Partitions

A partition of the positive integers into sets A and B avoids a set S N if no two distinct elements in the same part have a sum in S. If the partition is unique, S is uniquely avoidable. For any irrational > 1, Chow and Long constructed a partition which avoids the numerators of all convergents of the continued fraction for , and conjectured that the set S which this partition avoids is uniquely avoidable. We prove that the set of numerators of convergents is uniquely avoidable if and only if the continued fraction for has infinitely many partial quotients equal to 1. We also construct the set S and show that it is always uniquely avoidable.     

正向量连分式收敛的充分必要条件

我们讨论了如下形式的向量值连分式这里b_n=(b_n¹,b_n²,…,b_n^d)满足Samelson逆,而且a_n,b_n¹,b_n²,…,b_n^d均为正.给出了形如(#)的向量值连分式收敛的充分和必要条件,同时给出了收敛时的截断误差估计.     

关于两种连分式加速收敛方法等价性的一般猜想的证明

本文证明了［２］提出的两种连分式加速收敛方法等价性的一般猜想是正确的。     

集值映象重合点定理的进一步改进和推广

本文是文［１］的继续．在更一般的条件下，研究了完备度量空间中集值映象的重合点和不动点存在性问题