Convergence acceleration of non-scalar sequences with non-linear transformations

The rate of convergence of many sequences of numbers can be dramatically increased by non-linear sequence-to-sequence transformations. Several transformations of non scalar (vectorial or matricial) sequences are proposed in this paper. For a broad set of examples, their convergence accelerating properties are compared with those of other sequence transformation algorithms. The observed efficiency of some of the transformations introduced here seems to warrant a mathematical study.