关于Thiele型向量值连分式收敛定理的一个注记

A Note on Convergence Theorem for Thiele-Type Vector Valued Continued Fractions

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。

We improve the proof and results of Theorem 1 in [3] by means of the modified classical backward algorithm which is a generalization of the scalar case. We give also a more refined truncation error bound for this class of vector continued fractions under a slightly stronger condition.