Iterative difference three step
method with $1+\sqrt 2$ convergence rate

V. Ya. Bartish; N. Ph. Ogorodnyk

doi:10.15330/ms.43.2.220-224

The new three step method for solving unconstrained minimization problems is proposed. The method use the idea of building of three-step 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.

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. А. – 1972. – №7. – P. 579–582. (in Ukrainian)

4. Beyko I.V., Zin’ko 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. Three-step methods for soving unconstrained minimization problems// Visnyk Lviv. Univ., ser. Appl. Math. Inf. – 2007. – №13. – P. 3–10. (in Ukrainian)

6. Koko J. A conjugate gradient method with quasi-Newton approximation// Aplicationes mathematicae. – 2000. – №27. – P. 153–165.

	Iterative difference three step method with $1+\sqrt 2$ convergence rate (in Ukrainian)
Author	V. Ya. Bartish, N. Ph. Ogorodnyk 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 three-step 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.43.2.220-224
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. А. – 1972. – №7. – P. 579–582. (in Ukrainian) 4. Beyko I.V., Zin’ko 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. Three-step methods for soving unconstrained minimization problems// Visnyk Lviv. Univ., ser. Appl. Math. Inf. – 2007. – №13. – P. 3–10. (in Ukrainian) 6. Koko J. A conjugate gradient method with quasi-Newton approximation// Aplicationes mathematicae. – 2000. – №27. – P. 153–165.
Pages	220-224
Volume	43
Issue	1
Year	2015
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

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