Composite sequence transformations (Q1060521)

The concept of composite sequence transformations is introduced. Let \((S_ n)\) be a sequence to be accelerated and let S be its limit: Consider the p sequence transformations \[ t_ k: (S_ n)\to (t_ k^{(n)})\quad k=1,...,p \] and define the transformation T \[ T: (S_ n)\to (T_ n)\quad with\quad T_ n=\sum^{p}_{k=1}a_ k^{(n)}t_ k^{(n)}. \] T is called the composite sequence transformation and p is its rank. A number of results for composite sequence transformations is derived. It is proved that several known sequence transformations may be derived using this consept. Several numerical examples are given.