Gutiérrez, J. M.; Hernández, M. A.; Salanova, M. A. Accessibility of solutions by Newton’s method. (English) Zbl 0844.47035 Int. J. Comput. Math. 57, No. 3-4, 239-247 (1995). Summary: We give new conditions for the convergence of Newton’s method in Banach spaces, in terms of the degree of logarithmic convexity. These conditions guarantee the convergence of Newton sequence in cases where the hypothesis of the Kantorovich theorem are not verified, as we show in some examples. Cited in 38 Documents MSC: 47J25 Iterative procedures involving nonlinear operators 47H10 Fixed-point theorems 65J15 Numerical solutions to equations with nonlinear operators Keywords:convergence of Newton’s method in Banach spaces; degree of logarithmic convexity PDFBibTeX XMLCite \textit{J. M. Gutiérrez} et al., Int. J. Comput. Math. 57, No. 3--4, 239--247 (1995; Zbl 0844.47035) Full Text: DOI References: [1] DOI: 10.1137/0711002 · Zbl 0284.65042 · doi:10.1137/0711002 [2] Hernandez M. A., Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 22 pp 159– (1992) [3] DOI: 10.1080/00207169408804280 · Zbl 0824.65025 · doi:10.1080/00207169408804280 [4] Kantorovich L. V., Functional Analysis (1982) · Zbl 0484.46003 [5] Kreyszig E., Introductory Functional Analysis with applications (1978) · Zbl 0368.46014 [6] DOI: 10.2307/2321528 · Zbl 0407.65023 · doi:10.2307/2321528 [7] Ostrowski, A. M. 1943. ”Solution of equations in euclidean and Banach spaces”. Academic Press. [8] DOI: 10.1007/BF02843677 · Zbl 0193.43902 · doi:10.1007/BF02843677 [9] Rail L. B., Computational solution of nonlinear operator equations (1979) [10] DOI: 10.1007/BF01389624 · Zbl 0607.65033 · doi:10.1007/BF01389624 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.