Enlarging the radius of convergence for Newton–like method in which the derivative is re-evaluated after certain steps

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dc.citation.epage598
dc.citation.issue3
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage594
dc.contributor.affiliationУніверситет Кемерона
dc.contributor.affiliationЛьвівський національний університет імені Івана Франка
dc.contributor.affiliationCameron University
dc.contributor.affiliationIvan Franko National University of Lviv
dc.contributor.authorАргирос, К. І.
dc.contributor.authorАргирос, І. К.
dc.contributor.authorШахно, С. М.
dc.contributor.authorЯрмола, Г. П.
dc.contributor.authorArgyros, C. I.
dc.contributor.authorArgyros, I. K.
dc.contributor.authorShakhno, S. M.
dc.contributor.authorYarmola, H. P.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:32:57Z
dc.date.created2022-02-28
dc.date.issued2022-02-28
dc.description.abstractЗроблено спробу збільшити радіус області збіжності методу типу Ньютона за тих же умов, за яких метод вивчався раніше. Аналіз збіжності проведено за центральних та обмежених умов Ліпшиця. Крім радіусу області збіжності, вдалося отримати точніші оцінки похибки, а також більший радіус області єдиності розв’язку. Ці переваги є чисельно обґрунтованими.
dc.description.abstractNumerous attempts have been made to enlarge the radius of convergence for Newton–like method under the same set of conditions. It turns out that not only the radius of convergence but the error bounds on the distances involved and the uniqueness of the solution ball can more accurately be defined.
dc.format.extent594-598
dc.format.pages5
dc.identifier.citationEnlarging the radius of convergence for Newton–like method in which the derivative is re-evaluated after certain steps / C. I. Argyros, I. K. Argyros, S. M. Shakhno, H. P. Yarmola // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 594–598.
dc.identifier.citationenEnlarging the radius of convergence for Newton–like method in which the derivative is re-evaluated after certain steps / C. I. Argyros, I. K. Argyros, S. M. Shakhno, H. P. Yarmola // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 3. — P. 594–598.
dc.identifier.doidoi.org/10.23939/mmc2022.03.594
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63457
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 3 (9), 2022
dc.relation.ispartofMathematical Modeling and Computing, 3 (9), 2022
dc.relation.references[1] Măruşter Ş., Estimating local radius of convergence. Symposium “Symbolic and Numeric Algorithm for Scientific Computation” (SYNASC), Workshop Iteratime Approximation of Fixed Points, 24–27 Sept. 2016. West University of Timisoara, Timisoara, Romania (2016).
dc.relation.references[2] Măruşter Ş., On the local convergence of the Modified Newton method. Annals of West University of Timisoara – Mathematics and Computer Science. 57 (1), 13–22 (2019).
dc.relation.references[3] Potra F. A., Pt´ak V. Nondiscrete induction and iterative processes. Pitman Publ., London (1984).
dc.relation.references[4] Traub J. F. Iterative methods for the solution of equations. Chelsea Publishing Company, New York (1982).
dc.relation.references[5] Ortega J. M., Rheinboldt W. C. Iterative solution of nonlinear equation in several variables. Acad. Press, New York (1970).
dc.relation.references[6] Ezquerro J. A, Hern´andez M. A. An improvement of the region of accessibility of Chebyshev’s method from Newton’s method. Mathematics of Computation. 78 (267), 1613–1627 (2009).
dc.relation.references[7] Ezquerro J. A, Hern´andez M. A. An optimization of Chebyshev’s method. Journal of Complexity. 25 (4), 343–361 (2009).
dc.relation.references[8] Hern´andez-Veron M. A., Romero N. On the local convergence of a third order family of iterative processes. Algorithms. 8, 1121–1128 (2015).
dc.relation.references[9] C˘atina¸s E. Estimating the radius of an attraction ball. Applied Mathematics Letters. 22, 712–714 (2009).
dc.relation.references[10] Iakymchuk R. P., Shakhno S. M., Yarmola H. P. Convergence analysis of a two-step modification of the Gauss–Newton method and its applications. Journal of Numerical and Applied Mathematics. 126, 61–74 (2017).
dc.relation.references[11] Magre˜n´an A. A., Argyros I. K. Two-step Newton methods. Journal of Complexity. ´ 30 (4), 533–553 (2014).
dc.relation.references[12] Argyros I. K., Shakhno S. Extending the Applicability of Two-Step Solvers for Solving Equations. Mathematics. 7 (1), 62 (2019).
dc.relation.references[13] Argyros I. K., Magre˜n´an A. A. A Contemporary Study of Iterative Methods. Convergence, Dynamics and Applications. 333–346 (2018).
dc.relation.references[14] Shakhno S. M. On an iterative algorithm with superquadratic convergence for solving nonlinear operator equations. Journal of Computational and Applied Mathematics. 231 (1), 222–235 (2009).
dc.relation.references[15] Argyros I. K., Shakhno S., Yarmola H. Two-Step Solver for Nonlinear Equations. Symmetry. 11 (2), 128 (2019).
dc.relation.references[16] Kantorovich L. V., Akilov G. P. Functional Analysis. Oxford, Pergamon (1982).
dc.relation.referencesen[1] Măruşter Ş., Estimating local radius of convergence. Symposium "Symbolic and Numeric Algorithm for Scientific Computation" (SYNASC), Workshop Iteratime Approximation of Fixed Points, 24–27 Sept. 2016. West University of Timisoara, Timisoara, Romania (2016).
dc.relation.referencesen[2] Măruşter Ş., On the local convergence of the Modified Newton method. Annals of West University of Timisoara – Mathematics and Computer Science. 57 (1), 13–22 (2019).
dc.relation.referencesen[3] Potra F. A., Pt´ak V. Nondiscrete induction and iterative processes. Pitman Publ., London (1984).
dc.relation.referencesen[4] Traub J. F. Iterative methods for the solution of equations. Chelsea Publishing Company, New York (1982).
dc.relation.referencesen[5] Ortega J. M., Rheinboldt W. C. Iterative solution of nonlinear equation in several variables. Acad. Press, New York (1970).
dc.relation.referencesen[6] Ezquerro J. A, Hern´andez M. A. An improvement of the region of accessibility of Chebyshev’s method from Newton’s method. Mathematics of Computation. 78 (267), 1613–1627 (2009).
dc.relation.referencesen[7] Ezquerro J. A, Hern´andez M. A. An optimization of Chebyshev’s method. Journal of Complexity. 25 (4), 343–361 (2009).
dc.relation.referencesen[8] Hern´andez-Veron M. A., Romero N. On the local convergence of a third order family of iterative processes. Algorithms. 8, 1121–1128 (2015).
dc.relation.referencesen[9] C˘atina¸s E. Estimating the radius of an attraction ball. Applied Mathematics Letters. 22, 712–714 (2009).
dc.relation.referencesen[10] Iakymchuk R. P., Shakhno S. M., Yarmola H. P. Convergence analysis of a two-step modification of the Gauss–Newton method and its applications. Journal of Numerical and Applied Mathematics. 126, 61–74 (2017).
dc.relation.referencesen[11] Magre˜n´an A. A., Argyros I. K. Two-step Newton methods. Journal of Complexity. ´ 30 (4), 533–553 (2014).
dc.relation.referencesen[12] Argyros I. K., Shakhno S. Extending the Applicability of Two-Step Solvers for Solving Equations. Mathematics. 7 (1), 62 (2019).
dc.relation.referencesen[13] Argyros I. K., Magre˜n´an A. A. A Contemporary Study of Iterative Methods. Convergence, Dynamics and Applications. 333–346 (2018).
dc.relation.referencesen[14] Shakhno S. M. On an iterative algorithm with superquadratic convergence for solving nonlinear operator equations. Journal of Computational and Applied Mathematics. 231 (1), 222–235 (2009).
dc.relation.referencesen[15] Argyros I. K., Shakhno S., Yarmola H. Two-Step Solver for Nonlinear Equations. Symmetry. 11 (2), 128 (2019).
dc.relation.referencesen[16] Kantorovich L. V., Akilov G. P. Functional Analysis. Oxford, Pergamon (1982).
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectрадіус збіжності
dc.subjectметод типу Ньютона
dc.subjectгільбертів простір
dc.subjectradius of convergence
dc.subjectNewton–like method
dc.subjectHilbert space
dc.titleEnlarging the radius of convergence for Newton–like method in which the derivative is re-evaluated after certain steps
dc.title.alternativeЗбільшення радіусу збіжності методу типу Ньютона, в якому похідна обчислюється через декілька кроків
dc.typeArticle

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Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 3