Publication at Faculty of Mathematics and Physics |
2015
Abstract
In this paper, we construct several sequence transformations whose kernels contain sequences of the form S_n = S + a_n 位^n, n=0,1,..., where S and 位 are unknown parameters, and is a known sequence. These transformations generalize Aitken's process.
We provide certain sufficient conditions under which one of our transformations accelerates the convergence of certain types of sequences. Finally, we illustrate these theoretical results through several numerical experiments using diverging and converging sequences.