# On the two-step secant type method for solving nonlinear equations(in Ukrainian)

Author
Ivan Franko National University of Lviv
Abstract
In the paper the two-step secant type method for solving nonlinear operator equations under the generalized Lipschitz condition for divided difference is investigated. The convergence order and the radius of the convergence domain of the iterative process are established.
Keywords
nonlinear operator equation; iterative process; Lipschitz condition
Reference
1. Bartish M.Ya. About one iterative method of solving functional equations// Dop. AN URSR. Ser. A. – 1968. – V. 5. – P. 387–391. (in Ukrainian)

2. Bartish M.Ya., Shcherbyna Yu.M. About one difference method of solving operator equations// Dop. AN URSR. Ser. A. – 1972. – V.7. – P. 579–582. (in Ukrainian)

3. Kantorovich L.V., Akilov G.P. Functional analysis. Moscow: Nauka, 1984. (in Russian)

4. 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.

5. Shakhno S.M. Secant method under the generalized Lipschitz conditions for the first-order divided differences// Mathematical bulletin of the Shevchenko scientific society. – 2007. – V.4. – P. 296–305. (in Ukrainian)

6. Shakhno S.M. Convergence of the two-step Newton type method for solving of nonlinear equations under the generalized Lipschitz conditions// Physico-mathematical modelling and informational technologies. – 2012. – V.16. – Ð. 163–172. (in Ukrainian)

7. Shakhno S.M., Grab S.I., Yarmola H.P. Twoparametric secant type methods for solving nonlinear equations// Visnyk of the Lviv University. Series Applied Mathematics and Computer Science. – 2009. – V.15. – P. 117–127. (in Ukrainian)

8. 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.

9. Werner W. Uber ein Verfahren der Ordnung $1+\sqrt{2}$ zur Nullstellenbestimmung// Numer. Math. – 1979. – V.32. – P. 333–342.

Pages
84-88
Volume
42
Issue
1
Year
2014
Journal
Matematychni Studii
Full text of paper
Table of content of issue