Vector sequence transformations: Methodology and applications to linear systems

In this paper, a methodology for the construction of various vector sequence transformations is formulated leading to a unified presentation of the subject and to new results. The connections to the general interpolation problem and to projections are discussed. Various particular cases are examined in more details. Applications to the solution of systems of linear equations will end the paper and, in particular, their relation with Lanczos method will be studied. Some numerical examples will be given.