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Newton’s method under mild differentiability conditions with error analysis. (English) Zbl 0221.65084


MSC:

65J15 Numerical solutions to equations with nonlinear operators
65J99 Numerical analysis in abstract spaces
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References:

[1] Kantorovich, L. V., Akilov, G. P.: Functional analysis in normed spaces. Oxford: Pergamon Press 1964. · Zbl 0127.06104
[2] Keller, H. B.: Newton’s method under mild differentiability conditions, unpublished, 1965.
[3] Lancaster, P.: Error analysis for the Newton-Raphson method. Num. Math.9, 55 (1968). · Zbl 0173.17801 · doi:10.1007/BF02165230
[4] Moore, R. E.: Interval analysis. Englewood Cliffs, New Jersey: Prentice Hall 1966. · Zbl 0176.13301
[5] Rheinboldt, W. C.: A unified convergence theory for a class of iterative processes. SIAM J. Numer. Anal.5 1 (1968). · Zbl 0155.46701 · doi:10.1137/0705003
[6] Urabe, M.: Convergence of numerical iteration in solution of equations. J. Sci. Hiroshima Univ.19, 479 (1956). · Zbl 0072.14001
[7] Wilkinson, J. H.: The Algebraic eigenvalue problem. Oxford: Clarendon Press 1965. · Zbl 0258.65037
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