4. Application of Clifford algebra to projection-free vector convergence acceleration

In this section, it is shown that Clifford algebra applied to vector convergence acceleration methods is a powerful tool, easily overcoming the size difficulties outlined above, and leading to numerically more efficient methods. This is due to the fact that this approach using Clifford algebra avoids any projection and thus preserves all the characteristics of the terms of the vector sequence. We begin by introducing the ${\text{Δ}}^2$ Aitken vector, projection-free.