On the two-step secant type method for solving nonlinear equations(in Ukrainian) |
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Author |
s shakhno@franko.lviv.ua
Ivan Franko National University of Lviv
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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.
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Keywords |
nonlinear operator equation; iterative process; Lipschitz condition
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Reference |
1. Bartish M.Ya. About one iterative method of solving functional equations// Dop. AN URSR. Ser. A.
1968. V. 5. P. 387391. (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. 579582. (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. 222235. 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. 296305. (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. Π. 163172. (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. 117127. (in Ukrainian) 8. Wang X. Convergence of Newtons method and uniquiness of the solution of equations in Banach space// IMA Journal of Numerical Analysis. 2000. V.20. P. 123134. 9. Werner W. Uber ein Verfahren der Ordnung $1+\sqrt{2} $ zur Nullstellenbestimmung// Numer. Math. 1979. V.32. P. 333342. |
Pages |
84-88
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Volume |
42
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Issue |
1
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Year |
2014
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Journal |
Matematychni Studii
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Full text of paper | |
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