Numerical methods for solving nonlinear operator equations.

• Newtonian Methods in Nonlinear Problems (Informatics)
• Numerical Methods (System Analysis)
• Computational Methods of Linear Algebra (am, sa)
• Numerical Methods (am)

1. Argyros I.K. Extended convergence analysis of Newton-Potra solver for equations / I.K. Argyros, S.M. Shakhno, Yu.V. Shunkin, H.P. Yarmola // Journal of Numerical Analysis and Approximation Theory. – 2021. – Vol. 49, No. 2. – P. 100-112.
2. Argyros I.K. Semilocal convergence of a Newton-Secant solver for equations with a decomposition of operator / I.K. Argyros, S.M. Shakhno, H.P. Yarmola // Journal of Computational Analysis and Applications. – 2021. – Vol. 29, No. 2. – P. 279-289.
3. Argyros I.K. On methods with successive approximation of the inverse operator for nonlinear equations with decomposition of the operator/ I.K. Argyros, S.M. Shakhno, H.P. Yarmola // Вісник Львівського університету. Серія прикладна математика та інформатика. – 2020. – Випуск 28. – C. 3-14.
4. Argyros I.K. Method of Third-Order Convergence with Approximation of Inverse Operator for Large Scale Systems / I.K. Argyros, S.M. Shakhno, H.P. Yarmola // Symmetry. – 2020. – 12(6), 978.
5. Argyros I.K. Extending the Convergence Domain of Methods of Linear Interpolation for the Solution of Nonlinear Equations / I.K. Argyros, S.M. Shakhno, H.P. Yarmola // Symmetry. – 2020. – 12(7), 1093. 
6. Argyros I. K. On an improved convergence analysis of a two-step Gauss-Newton type method under generalized Lipschitz conditions / I.K. Argyros, R.P. Iakymchuk, S.M. Shakhno, H.P. Yarmola // Carpathian Journal of Mathematics. – 2020. – Vol. 36 , No. 3. – P. 365-372.
7. Argyros I.K. Improving Convergence Analysis of the Newton–Kurchatov Method under Weak Conditions / I.K. Argyros, S.M. Shakhno, H.P. Yarmola // Computation. – 2020. – 8(1), 8.
8. Argyros I.K. Extended semilocal convergence for the Newton-Kurchatov method / I.K. Argyros, S.M. Shakhno, H.P. Yarmola // Matematychni Studii. – 2020. – Vol. 53, №.1. – P. 85-91.
9. Argyros I.K. Local convergence analysis of the Gauss-Newton-Kurchatov method / I.K. Argyros, S.M. Shakhno, H.P. Yarmola // Mathematical Modeling and Computing. – 2020. – Vol. 7, No. 2. – P. 248-258.
10. Шахно С.М. Метод Гаусса-Ньютона-Потра для нелiнiйних задач найменших квадратів за узагальнених умов Лiпшиця / С.М. Шахно, Ю.В. Шунькін, Г.П. Ярмола // Вісник Львівського університету. Серія прикладна математика та інформатика. – 2019. – Випуск 27. – C. 40-49.
11. Ярмола Г.П. Чисельне розв’язування задачі Дiрiхле для рівняння Гельмгольца за допомогою різницевих схем підвищеного порядку / Г.П. Ярмола, А.Т. Дудикевич // Вісник Львівського університету. Серія прикладна математика та інформатика. – 2019. – Випуск 27. – C. 50-55.
12. Shakhno S.M. Convergence of the Newton-Kurchatov method under weak conditions / S.M. Shakhno, H.P. Yarmola // Journal of Mathematical Sciences. – 2019. – Vol. 243, №. 1. – P. 1-10.
13. Argyros I.K. Two-step solver for nonlinear equations / I.K. Argyros, S. Shakhno, H.Yarmola // Symmetry. – 2019. – Vol. 11, Iss. 2, 128.
14. Argyros I.K. Two-step solver for equations with nondifferentiable term / I.K. Argyros, S. Shakhno, H. Yarmola // International Journal of Applied and Computational Mathematics. – 2019. – Vol. 5, Iss.3.
15. Iakymchuk R. Gauss-Newton-Secant method for solving nonlinear least squares problems / R. Iakymchuk, H. Yarmola, S. Shakhno // PAMM Proc. Appl. Math. Mech. – 2018. – Vol. 18, Iss. 1. – P. 1-2.
16. Shakhno S.M. Convergence analysis of the Gauss-Newton-Potra method for nonlinear least squares problems / S. M. Shakhno, H.P. Yarmola, Yu.V. Shunkin // Matematychni Studii. – 2018. – Vol. 50, №.2. – P. 211-221.
17. Shakhno S. Gauss-Newton-Potra method for nonlinear least squares problems with decomposition of operator / S. Shakhno, H. Yarmola, Yu. Shunkin // XXXII International Conference PDMU-2018: Problems of Decision Making Under Uncertainties: Prague, Czech Republic, August 27-31, 2018: Proceedings. – 2018. – P. 153-159.
18. Shakhno S.M. Convergence analysis of a two-step method for the nonlinear least squares problem with decomposition of operator / S.M. Shakhno, R.P. Iakymchuk, H.P. Yarmola // Journal of Numerical and Applied Mathematics. – 2018. – Vol. 128, № 2. – P. 82-95.
19. Iakymchuk R.P. Convergence analysis of a two-step modification of the Gauss-Newton method and its applications / R.P. Iakymchuk, S.M. Shakhno, H.P. Yarmola // Journal of Numerical and Applied Mathematics. – 2017. – Vol. 126, № 3. – P. 61-74.
20. Shakhno S.M. An iterative method for solving nonlinear least squares problems with nondifferentiable operator / S.M. Shakhno, R.P. Iakymchuk, H.P. Yarmola // Matematchni Studii. – 2017. – Vol. 48, № 1. – 97-107.
21. Шахно С. Про збіжність методу Ньютона-Потра за слабких умов / С.М. Шахно, Г.П. Ярмола // Вісник Львівського університету. Серія прикладна математика та інформатика. – 2017. – Випуск 25. – С. 49-55
22. Шахно С.М. Збіжність методу Ньютона-Курчатова за слабких умов / С.М. Шахно, Г.П. Ярмола // Мат. методи та фіз.-мех. поля. – 2017. – T 60, № 2. – С. 7-13.
23. Iakymchuk R. Combined Newton-Kurchatov method for solving nonlinear operator equations / R. Iakymchuk, S.Shakhno, H. Yarmola // PAMM – Proc. Appl. Math. Mech. – 2016. – 16 (1). – P. 719-720. / DOI: 10.1002/pamm.201610348.
24. Shakhno S.M. Analysis of the convergence of a combined method for the solution of nonlinear equations / S.M. Shakhno, I.V.Mel’nyk, H.P.Yarmola // Journal of Mathematical Sciences. – 2014. – 201, No. 1. – P.32-43.
25. Shakhno S.M. On the two-step method for solving nonlinear equations with nondifferentiable operator / S.M. Shakhno, H.P. Yarmola // PAMM – Proc. Appl. Math. Mech. – 2012. – V. 12. – P. 617 – 618. – doi 10.1002/pamm.201210297.
26. Shakhno S.M. Two-step combined method for solving nonlinear operator equations / S.M. Shakhno, H.P.Yarmola // Journal of Numerical and Applied Mathematics. – 2014. – № 2 (116). – С. 130-140.
27. Shakhno S. Two-step method for solving nonlinear equations with nondifferentiable operator / S. Shakhno, H. Yarmola // Journal of Numerical and Applied Mathematics. – 2012. – № 3(109). – С.105–115.
28. Shakhno S.M. Convergence conditions of the two-parametric secant type method for solving nonlinear equations taking into account errors / S.M. Shakhno, H.P.Yarmola // Taurida Journal of Computer Science Theory and Mathematics . – 2013. – Vol. 2. – P. 137-145.
29. Yarmola H.P. Difference methods for solving inverse eigenvalue problem / H.P. Yarmola // Journal of Numerical and Applied Mathematics. – 2015. – №2 (119). – P. 101-106.

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