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A generalized Newton method for absolute value equations
Optimization Letters, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Rate of convergence of a generalization of Newton's method
Journal of Optimization Theory and Applications, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Benadada, Y. +2 more
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Generalized Stirling-Newton Methods
1976In this contribution we generalize Newton’s method and related methods for the solution of fixed point problems. We replace the linear approximations to a given nonlinear operator which result from differentiability assumptions by arbitrary “tangent” mappings. Therefore our iteration algorithms apply to nondifferentiable operators.
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On a general iterative scheme for newton-type methods
Numerical Functional Analysis and Optimization, 1988A class of Newton-type iterative processes for solving nonlinear operator equations in Banach spaces is described by a general scheme, in which the approximate inverses of the derivatives are obtained recursively. Convergence conditions as well as error estimates are given. Some particular cases are finally discussed.
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Newton's method in generalized banach spaces
Numerical Functional Analysis and Optimization, 1987A Kantorowitsch-analysis of Newton's method in generalized Banach spaces is given. The application of generalized norms – mappings from a linear space into a partially ordered Banach space - improves convergence results and error estimatescompared with the real norm theory.
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On the generation of updates for quasi-Newton methods
Journal of Optimization Theory and Applications, 1986We present a unified technique for updating approximations to Jacobian or Hessian matrices when any linear structure can be imposed. The updates are derived by variational means, where an operator-weighted Frobenius norm is used, and are finally expressed as solutions of linear equations and/or unconstrained extrema. A certain behavior of the solutions
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Generalized Newton-Raphson method (GNR)
International journal of mathematical sciences, 2012We present a new method for solving a non-linear equation f(x)=0. The presented method is quadratically convergent, it converges faster than the classical Newton-Raphson method and the Newton- Raphson method appears as the limiting case of the presented method.
Sandrić, Nikola, Viher, Radimir
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On a generalization of the method of Newton - kantorovich
Ukrainian Mathematical Journal, 1972openaire +1 more source