Application of Aitken’s extrapolation in numerical analysis

The paper is a continuation and elaboration of the subject of [5], which investigated the application of algorithm Ɛ and Aitken’s extrapolation to solve large sets of linear equations. In this paper the application of algorithm Ɛ [1], [2] was abandoned since in the following examples under study it yielded worse results than Aitken’s extrapolation. The acceleration of sequence (xn) convergence through Aitken’s extrapolation consists in creating sequence (x'n) given by dependence: ...[wzór] which is convergent faster than the sequence (xn) [1], [2], [4]. To the sequence (x'n) formula (1) can be once more applied, which is referred to as multiple Aitken’s extrapolation and can be written as: ...[wzór]