Hybrid vector transformations

We present in this paper hybrid and semi-hybrid vector extrapolation methods. For a vector sequence transformation, we will define the generalized residual which allows us to introduce a new hybrid vector transformation. When solving linear systems, this new transformation reduces to the hybrid procedure defined by Brezinski and Redivo Zaglia (1994) which is a generalization of the smoothing technique. In the second part of this paper, we define a new composite transformation called semi-hybrid. When applied to linearly generated sequences, we will show that the residual polynomial of the semi-hybrid transformation is the product of two residual polynomials.