Improved convergence and complexity analysis of Newton's method for solving equations

Authors:
Ioannis K. Argyros
Affiliations:
Department of Mathematical Sciences, Cameron University, Lawton, OK, USA
Venue:
International Journal of Computer Mathematics
Year:
2007

Citing 3
Cited 0

A convergence theorem for Newton-like methods in Banach spaces

Numerische Mathematik
Convergence and Complexity of Newton Iteration for Operator Equations

Journal of the ACM (JACM)
Iterative solution of nonlinear equations in several variables

Iterative solution of nonlinear equations in several variables

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Abstract

A finer optimal convergence condition for the local convergence of Newton's method is obtained using more precise error estimates. A condition for finer computational complexity is also obtained.