3. Rational extrapolation

Let (S _n ) be a sequence of numbers, vectors or matrices that converges to S. When its convergence is slow, we transform it, without modifying it, into a new sequence (T _n ) which, under certain assumptions, converges faster to the same limit, i.e. such that

\lim_{n \to \infty} \frac{‖ T_{n} - S ‖}{‖ S_{n} - S ‖} = 0 .

Such methods are called sequence transformations...

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Bibliography

(1) - BAKER (G.A.) Jr., GRAVES-MORRIS (P.R.) - Padé Approximants - 2 ^nd ed., Cambridge University Press, Cambridge (1996).
(2) - BERRUT (J.-P.), BALTENSPERGER (R.), MITTELMANN (H.D.) - . – Recent developments...

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