Increasing the interval of convergence for a generalized Newton’s method of solving nonlinear equations


  • A.N. Gromov


iterative processes
Newton’s method
logarithmic derivative
continuous functions defined on a segment
higher order methods
interval of convergence
transcendental equations


An approach to the construction of an extended interval of convergence for a previously proposed generalization of Newton’s method to solve nonlinear equations of one variable. This approach is based on the boundedness of a continuous function defined on a segment. It is proved that, for the search for the real roots of a real-valued polynomial with complex roots, the proposed approach provides iterations with nonlocal convergence. This result is generalized to the case transcendental equations.





Section 1. Numerical methods and applications

Author Biography

A.N. Gromov

Odintsovo University for the Humanities, Department of Economics
• Associate Professor


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