Geodesic
Notes on Numerical Analysis IV. On Accelerating Iteration Procedures With Superlinear Convergence
Canadian mathematical bulletin, Tome 7 (1964) no. 3, pp. 425-430

Voir la notice de l'article provenant de la source Cambridge University Press

In the study of algorithms for the iterative solution of an arbitrary analytic equation f(z) = 0, acceleration procedures are of importance in practice and of considerable interest in the theory of the subject. Let .be an iteration formula which has a zero ξ of f(z) as attractive fixed point. An algorithm of this type is said to converge towards a root ξ of f(z) = 0 for all initial approximations z = z0 in a vicinity of ξ, of order k > 0, when 1 . 
Kotzé, Wesley. Notes on Numerical Analysis IV. On Accelerating Iteration Procedures With Superlinear Convergence. Canadian mathematical bulletin, Tome 7 (1964) no. 3, pp. 425-430. doi: 10.4153/CMB-1964-041-1
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