Relaxing Convergence Conditions for Newton's Method
Copyright policy )Relaxing Convergence Conditions for Newton's Method
The classical Kantorovich theorem on Newton's method assumes that the first derivative of the operator involved satisfies a Lipschitz condition ∥Γ0[F′(x)-F′(y)]∥≤L∥x-y∥. In this paper, we weaken this condition, assuming that ∥Γ0[F′(x)-F′(x0)]∥≤ω(∥x-x0∥) for a given point x0. © 2000 Academic Press.
- University of La Rioja Spain
Other nonlinear integral equations, iterative processes, Banach space, convergence, Numerical solutions to equations with nonlinear operators, Applied Mathematics, nonlinear operator equation, nonlinear Hammerstein equation, error estimate, Numerical methods for integral equations, Kantorovich theorem, Newton's method, Iterative procedures involving nonlinear operators, Newton method, Iterative processes, Lipschitz condition, Analysis, Kantorovich conditions
Other nonlinear integral equations, iterative processes, Banach space, convergence, Numerical solutions to equations with nonlinear operators, Applied Mathematics, nonlinear operator equation, nonlinear Hammerstein equation, error estimate, Numerical methods for integral equations, Kantorovich theorem, Newton's method, Iterative procedures involving nonlinear operators, Newton method, Iterative processes, Lipschitz condition, Analysis, Kantorovich conditions
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