New vector sequence transformations

Many numerical methods produce sequences of vectors converging to the solution of a problem. When the convergence is slow, the sequence can be transformed into a new vector sequence which, under some assumptions, converges faster to the same limit. The construction of a sequence transformation is based on its kernel, that is the set of sequences which are transformed into a constant sequence. In this paper, new vector sequence transformations are built from kernels which extent those of the most general transformations known so far.