Iterative difference three step method with $1+\sqrt 2$ convergence rate (in Ukrainian) 

Author 
gut.natalochka@gmail.com, ktop@franko.lviv.ua
Ivan Franko National University of Lviv

Abstract 
The new three step method for solving unconstrained minimization problems is proposed.
The method use the idea of building of threestep methods and is based on a method with the rate of convergence $1+\sqrt 2$.
The rate of convergence for the new method is investigated.
Numerical investigation is conducted on the test functions. The result of numerical experiments
shows that three step method is more effective in sense of amount of calculations.
The efficiency of the method is growing with increasing of function's dimension.

Keywords 
tree step method; minimization problem

DOI 
doi:10.15330/ms.43.2.220224

Reference 
1. Vasiljev F.P. Numerical methods for solving extremal problems. M.: Nauka, 1988. 552 p. (in Russian)
2. Pshenichnyj B.N., Danilin Yu.M. Numerical methods in extremal problems. M.: Nauka, 1975. 319 p. (in Russian) 3. Bartish M.Ya., Shcherbyna Yu.M. On a difference method for solving nonlinear operator equations// Dop. AN USSR., ser. ΐ. 1972. Ή7. P. 579582. (in Ukrainian) 4. Beyko I.V., Zinko P.M., Nakonechnyj O.G. Problems methods and algorithms optimization. VGC.: Kyiv. Univ., 2012. 800 p. (in Ukrainian) 5. Bartish M.Ya., Kovalchuk O.V., Ogorodnyk N.P. Threestep methods for soving unconstrained minimization problems// Visnyk Lviv. Univ., ser. Appl. Math. Inf. 2007. Ή13. P. 310. (in Ukrainian) 6. Koko J. A conjugate gradient method with quasiNewton approximation// Aplicationes mathematicae. 2000. Ή27. P. 153165. 
Pages 
220224

Volume 
43

Issue 
1

Year 
2015

Journal 
Matematychni Studii

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