Two-point method for solving nonlinear equation with nondifferentiable operator (in Ukrainian)

Author S. M. Shakhno, H. P. Yarmola

Lviv Ivan Franko National University

Abstract In the paper we study a combined differential-difference method for solving nonlinear equations with non-differentiable operator. The semilocal convergence of the method is investigated and the order of convergence is established.
Keywords nonlinear equation; differential-difference method; semilocal convergence; non-differentiable operator
Reference 1. Kurchatov V.A. On one method of linear interpolation for solving functional equations // Dokl. AN SSSR. Ser. Mathematics. Physics. – 1971. – V.198.– №3. – P. 524–526. (in Russian)

 2. Ortega J.M., Rheinboldt W.C. Iterative solution of nonlinear equations in several variables. – Academic Press, New York, 1970.

 3. Traub J.F. Iterative methods for the solution of equations. – Prentice Hall, Englewood Cliffs, 1964.

 4. Shakhno S.M. On the difference method with quadratic convergence for solving nonlinear operator equations// Mat. Stud. – 2006. – V.26. – P. 105–110. (in Ukrainian)

 5. Amat S., Busquier S. A modified secant method for semismooth equations // Appl. Math. Lett. – 2003. – V.16. – P. 877–881.

 6. Argyros I.K. A unifying local-semilocal convergenceanalysis and applications for two-point Newton-like methods in Banach space// J. Math. Anal. Appl. – 2004. – V.298. – P. 374–397.

 7. Argyros I.K. Improving the rate of convergence of Newton methods on Banach spaces wth a convergence structure and applications// Appl. Math. Lett. – 1997. – V.6. – P. 21–28.

 8. Сhen X. On the convergence of Broyden-like methods for nonlinear equations with nondifferentiable terms// Ann. Inst. Statist. Math. – 1990. – V.42, №2. – P. 387–401.

 9. Hernandez M.A., Rubio M.J. The Secant method for nondifferentiable operators// Appl. Math. Lett. – 2002. – V.15. – P. 395–399.

 10. Ren H., Argyros I.K. A new semilocal convergence theorem for a fast iterative method with nondifferentiable operators// J. Appl. Math. Comp. – 2010. – V.34. – №1-2. – P. 39–46.

 11. Shakhno S.M. On an iterative algorithm with superquadratic convergence for solving nonlinear operator equations// J. Comp. App. Math. – 2009. – V.231. – P. 222–235.

 12. Wang X. Convergence of Newton’s method and uniquiness of the solution of equations in Banach space// IMA Journal of Numerical Analysis. – 2000. – V.20. – P. 123–134.
Pages 213-220
Volume 36
Issue 2
Year 2011
Journal Matematychni Studii
Full text of paper PDF
Table of content of issue HTML