正向量连分式收敛的充分必要条件

Necessary and Sufficient Conditions for Convergence of Vector Continued Fractions with Positive Elements

中文关键词:  向量值连分式  收敛  截断误差估计

英文关键词:vector valued continued fractions  convergence  truncation error estimation.

中文摘要:

      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.

英文摘要:

      Vector valued continued fractions of the formare considered, where b_n= (b_n¹,b_n²,…,b_n^d) satisfy Samelson inverse and a_n, b_n¹,b_n²,…,b_n^d are positive. A few necessary and sufficient conditions for the convergence of (#) are obtained. Moreover, a truncation error estimation is given.