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

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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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     author = {Kotz\'e, Wesley},
     title = {Notes on {Numerical} {Analysis} {IV.} {On} {Accelerating} {Iteration} {Procedures} {With} {Superlinear} {Convergence}},
     journal = {Canadian mathematical bulletin},
     pages = {425--430},
     year = {1964},
     volume = {7},
     number = {3},
     doi = {10.4153/CMB-1964-041-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1964-041-1/}
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