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Optimization of the convergence order for a modification of Newton’s method. (English. Russian original) Zbl 0664.65046

J. Sov. Math. 43, No. 3, 2468-2469 (1988); translation from Issled. Prikl. Mat. 7, 75-77 (1979).
See the review in Zbl 0439.65030.

MSC:

65H05 Numerical computation of solutions to single equations

Citations:

Zbl 0439.65030
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References:

[1] J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York (1970). · Zbl 0241.65046
[2] V. A. Varyukhin and S. A. Kas’yanyuk, ?Iterative methods of determining the roots of equations more accurately,? Zh. Vychisl. Mat. Mat. Fiz.,9, 684?687 (1969).
[3] O. Kh. Tikhonov, ?Fast computation of the greatest roots of a polynomial,? Zap. Leningr. Gorn. Inst.,48, No. 3, 36?41 (1968).
[4] L. N. Dordevic, ?An iterative solution of algebraic equations with a parameter to accelerate convergence,? Pull. Elektrotek. Jak. Unit. Beogradu. Ser. Mat. Fiz., No. 412?460, 179?182 (1973). · Zbl 0282.65040
[5] A. P. Domoryad, ?Numerical and graphic methods of solution of equations,? in: Matmaticheskaia Entsiklopediya, Vol. 2 [in Russian], Gos. Izd. Tekhniko-Teoret. Liter., Moscow (1951).
[6] G. S. Salekhov, ?Convergence of the process of tangent hyperbolas for general functional equations,? Dokl. Akad. Nauk SSSR,82, No. 4, 525?528 (1952).
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