3. Clifford algebra

Unlike the extensions of the Shanks transformation in the previous section, the extensions we wish to build must avoid any projection, so that the information contained in each vector term of the sequence is completely preserved. One might expect the results obtained in this way to be much better than those obtained by projection, and this is actually the case. To achieve this, we need to find a different way of treating the system linked to the Shanks transformation, involving a sequence of vectors. The aim is to eliminate the difficulty related to the size of the system (number of constraints far greater than the number of freedoms). The introduction of universal Clifford algebra is a formidable tool for this purpose. This is the subject of the following sections.

• Universal Clifford algebra $$