Etudes sur les ε- et ρ-algorithmes
Tóm tắt
Some methods of accelerating the convergence of sequences are studied herein. It is shown that, in some special cases, the convergence of the ε-algorithm of Wynn is assured. A modification of this algorithm is then proposed which may still accelerate the convergence toward the limit. Finally, a new ϱ-algorithm is given in which the dependence with respect to a parameter is explicitely introduced.
Tài liệu tham khảo
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Aitken, A. C.: Determinants and matrices. Oliver and Boyd 1951.
Shanks, D.: Non-linear transformations of divergent and slowly convergent sequences. J. Math. and Phys.34, 1–42 (1955).
Wynn, P.: On a procrustean technique for the numerical transformation of slowly convergent sequences and series. Proc. Camb. Phil. Soc.52, 663–671 (1956).
—: On the convergence and stability of the epsilon algorithm. SIAM Num. Anal.3, 91–122 (1966).
—: On a device for computing thee m (S n ) transformation. MTAC10, 91–96 (1956).
Wynn, P.: Communication privée.