New solutions of equations on
New sufficient convergence conditions for the secant method
We provide new sufficient conditions for the convergence of the secant method to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses “Lipschitz-type” and center-“Lipschitz-type” instead of just “Lipschitz-type” conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than the earlier ones and under our convergence hypotheses we can cover cases where the earlier conditions are violated.
New unifying convergence criteria for Newton-like methods
We present a local and a semilocal analysis for Newton-like methods in a Banach space. Our hypotheses on the operators involved are very general. It turns out that by choosing special cases for the "majorizing" functions we obtain all previous results in the literature, but not vice versa. Since our results give a deeper insight into the structure of the functions involved, we can obtain semilocal convergence under weaker conditions and in the case of local convergence a larger convergence radius....
New variational principle and duality for an abstract semilinear Dirichlet problem
A new variational principle and duality for the problem Lu = ∇G(u) are provided, where L is a positive definite and selfadjoint operator and ∇G is a continuous gradient mapping such that G satisfies superquadratic growth conditions. The results obtained may be applied to Dirichlet problems for both ordinary and partial differential equations.
Newton-Kantorovich method and its global convergence.
Newton's methods for variational inclusions under conditioned Fréchet derivative
Estimates of the radius of convergence of Newton's methods for variational inclusions in Banach spaces are investigated under a weak Lipschitz condition on the first Fréchet derivative. We establish the linear convergence of Newton's and of a variant of Newton methods using the concepts of pseudo-Lipschitz set-valued map and ω-conditioned Fréchet derivative or the center-Lipschitz condition introduced by the first author.
Newton-type iterations as approximations of Chebyshev's method.
Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations
We use a combination of modified Newton method and Tikhonov regularization to obtain a stable approximate solution for nonlinear ill-posed Hammerstein-type operator equations KF(x) = y. It is assumed that the available data is with , K: Z → Y is a bounded linear operator and F: X → Z is a nonlinear operator where X,Y,Z are Hilbert spaces. Two cases of F are considered: where exists (F’(x₀) is the Fréchet derivative of F at an initial guess x₀) and where F is a monotone operator. The parameter...
Nichtlineare analytische Eigenwertprobleme im Banachraum.
Nichtlineare Eigenwertprobleme mit zwei Parametern.
Nichtlineare Störung der isolierten Eigenwerte selbstadjungierter Operatoren.
Nodal solutions for a second-order -point boundary value problem
We study the existence of nodal solutions of the -point boundary value problem where
Nonautonomous functional equations and nonlinear evolution operators
Non-compact random generalized games and random quasi-variational inequalities.
Non-convex perturbations of evolution equations with -dissipative operators in Banach spaces
Non-degenerate implicit evolution inclusions.
Nondiscrete induction and an inversion-free modification of Newton's method
Nondiscrete induction and double step secant method.
Nonexpansive mappings and iterative methods in uniformly convex Banach spaces.
Nonlinear analysis. New arguments and results.
Si presentano condizioni sufficienti in forma astratta per l'esistenza di soluzioni di equazioni operazionali non lineari la cui parte lineare non è autoaggiunta.