2. Concrete problem

The need to extend these scalar concepts to vector sequences is trivial. It is always possible to simply apply these transformations to the components of the vector sequence. This approach is of little interest. It doesn't consider a vector as a whole, but just as a succession of independent components. The calculation does not involve interactions between the components of a vector. This will become clearer later on.

2.1 1st-order Shanks transformation for vectors, by projection

Now consider a vector sequence $(s_{n})$ where the term $s_{n} \in ℝ^{d}$ ...

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Bibliography

(1) - SHANKS (D.) - Non linear transformations of divergent and slowly convergent sequences. - J. Math. Phys., 34 : 1–42 (1955).
(2) - AITKEN (A.C.) - On Bernoulli's numerical solution of algebraic equations. - Proc. R. Soc. Edinb., 46 : 289–305...

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