Convergence of the Newton-Kantorovich method under Vertgeim conditions: A new improvement

DOI10.4171/ZAA/821zbMath0907.65054MaRDI QIDQ1393090

Espedito De Pascale, Peter P. Zabreĭko

Publication date: 30 September 1998

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

zbMATH Keywords

convergenceBanach spacesnonlinear integral equationsNewton-Kantorovich methoditerative solutionabstract nonlinear equationsHölder type conditions

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Numerical solutions to equations with nonlinear operators (65J15)

Related Items

Improved estimates on majorizing sequences for the Newton-Kantorovich method ⋮ Weaker convergence for Newton's method under Hölder differentiability ⋮ New general convergence theory for iterative processes and its applications to Newton-Kantorovich type theorems ⋮ Convergence of Newton's method under Vertgeim conditions: new extensions using restricted convergence domains ⋮ Estimates of majorizing sequences in the Newton-Kantorovich method: a further improvement ⋮ Concerning the ``terra incognita between convergence regions of two Newton methods ⋮ Newton–Kantorovich Approximations When the Derivative Is Hölderian: Old and New Results ⋮ On Convergence Domains of Newton's and Modified Newton Methods ⋮ Estimates of Majorizing Sequences in the Newton–Kantorovich Method ⋮ On the weakening of the convergence of Newton's method using recurrent functions ⋮ On solution of nonlinear singular integral equations with shift in generalized Hölder space

Cites Work

• New convergence criteria for the Newton-Kantorovich method and some applications to nonlinear integral equations
• New results on newton-kantorovich approximations with applications to nonlinear integral equations
• On the application of the newton-kantorovich method to nonlinear integral equations of uryson type
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