The T +m Transformation
Roland F. Streit · Mathematics of Computation · 1976
This paper discusses a nonlinear sequence-to-sequence transformation, known as the T+m transform, which is used to accelerate the convergence of an infilnite series. A brief history of the transform is given; a number of theorems are established which enable one to make effective use of the transform, and several examples are presented to illustrate this effectiveness. This paper discusses a nonlinear sequence-to-sequence transformation, known as the T+m transformation, which is used to accelerate the convergence of an infinite series. A brief historical sketch of the transformation is given and a number of theorems are established which enable one to make effective use of the T+m transform. In particular, special attention is given to the case in which the transformed series con- verges more rapidly or uniformly better than the original series. Finally, several examples are given to illustrate the effectiveness of the transformation. The T+ 1 transformation was found independently by many authors. Generally, it was applied to some slowly convergent sequences for the purpose of accelerating their convergence. These sequences arose as a consequence of either (a) some iterative process or (b) as the partial sums of an infinite series.