본문 바로가기
KERD
논문KCI 등재

Improved local convergence analysis for a three point method of convergence order 1.839$\dots$

조열제|Ioannis K. Argyros|Santhosh George
대한수학회 (The Korean Mathematical Society)|2019.05|대한수학회보 (Bulletin of the KMS)|제56권 제3호|pp. 621-629|DOI 10.4134/BKMS.b180429

2

조회

0

다운로드

0

인용

0

참고문헌

키워드

Banach spacelocal convergenceradius of convergencethree point methoddivided difference of order one-two
주제분류수학

초록

In this paper, we present a local convergence analysis of a three point method with convergence order 1.839$\dots$ for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results.

Abstract

In this paper, we present a local convergence analysis of a three point method with convergence order 1.839$\dots$ for approximating a locally unique solution of a nonlinear operator equation in setting of Banach spaces. Using weaker hypotheses than in earlier studies, we obtain: larger radius of convergence and more precise error estimates on the distances involved. Finally, numerical examples are used to show the advantages of the main results over earlier results.

참고문헌 (26)

  1. S. Amat, "Geometric constructions of iterative func-tions to solve nonlinear equations", J. Comput. Appl. Math, 157(1), pp.197~205 (2003)
  2. I. K. Argyros, "A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space", J. Math. Anal. Appl, 298(2), pp.374~397 (2004)
  3. I. K. Argyros, "Computational Theory of Iterative Methods" (2007), Elsevier Publ. Co
  4. I. K. Argyros, "A semilocal convergence analysis for directional Newton methods", Math. Comp, 80(273), pp.327~343 (2011)
  5. Ioannis Konstantinos Argyros, "ON THE “TERRA INCOGNITA” FOR THE NEWTON-KANTROVICH METHOD WITH APPLICATIONS", 대한수학회지, 51(2), pp.251~266 (2014), 대한수학회
  6. I. K. Argyros, "Numerical methods for equations and its appli-cations" (2012), CRC Press
  7. I. K. Argyros, "Convergence of Halley's method for operators with the bounded second Frechet-derivative in Banach spaces", J. Inequal. Appl, 2013(260), pp.12~ (2013)
  8. I. K. Argyros, "Weaker conditions for the convergence of Newton's method", J. Complexity, 28(3), pp.364~387 (2012)
  9. I. K. Argyros, "Computational Methods in Nonlinear Analysis" (2013), World Scientic Publishing Co. Pte. Ltd.
  10. R. Behl, "On developing fourth-order optimal families of methods for multiple roots and their dynamics", Appl. Math. Comput, 265, pp.520~532 (2015)
  11. V. Candela, "Recurrence relations for rational cubic methods: I. The Halley method", Computing, 44(2), pp.169~184 (1990)
  12. V. Candela, "Recurrence relations for rational cubic methods. II. The Chebyshev method", Computing, 45(4), pp.355~367 (1990)
  13. C. Chun, "Third-order family of methods in Banach spaces", Comput. Math. Appl, 61(6), pp.1665~1675 (2011)
  14. J. M. Gutierrez, "Third-order iterative methods for operators with bounded second derivative", J. Comput. Appl. Math, 82(1-2), pp.171~183 (1997)
  15. J. M. Gutierrez, "Recurrence relations for the super-Halley method", Comput. Math. Appl, 36(7), pp.1~8 (1998)
  16. M. A. Hernandez, "Chebyshev's approximation algorithms and applications", Comput. Math. Appl, 41, pp.433~455 (2001)
  17. M. A. Hernandez, "Modication of the Kantorovich assumptions for semilocal convergence of the Chebyshev method", J. Comput. Appl. Math, 126(1-2), pp.131~143 (2000)
  18. L. V. Kantorovich, "Functional Analysis" (1982), Pergamon Press
  19. A. Magre~nan, "Dierent anomalies in a Jarratt family of iterative root-nding methods", Appl. Math. Comput, 233, pp.29~38 (2014)
  20. A. Magrenan, "A new tool to study real dynamics: the convergence plane", Appl. Math. Comput, 248, pp.215~224 (2014)
  21. A. Magrenan, "A contemporary study of iterative methods" (2018), Academic Press
  22. J. M. Ortega, "Iterative Solution of Nonlinear Equations in Several Variables" (1970), Academic Press
  23. P. K. Parida, "Recurrence relations for semilocal convergence of a Newton-like method in Banach spaces", J. Math. Anal. Appl, 345(1), pp.350~361 (2008)
  24. M. S. Petkovic, "Multipoint Methods for Solving Nonlinear Equations", pp.2013, Elsevier
  25. F. A. Potra, "On an iterative algorithm of order 1:839...for solving nonlinear operator equations", Numer. Funct. Anal. Optim, 7(1), pp.75~106 (1985)
  26. J. R. Sharma, "Ecient Jarratt-like methods for solving systems of non-linear equations", Calcolo, 51(1), pp.193~210 (2014)

관련 논문AI추천

Local convergence for some third-order iterative methods under weak conditions조열제, Ioannis K. Argyros, Santhosh George대한수학회 · 대한수학회지2016 · 제53권 제4호IMPROVED CONVERGENCE OF STEFFENSEN’S METHOD FOR APPROXIMATING FIXED POINTS OF OPERATORS IN BANACH SPACEHongmin Ren, Ioannis K. Argyros대한수학회 · 대한수학회지2017 · 제54권 제1호ON THE SEMILOCAL CONVERGENCE OF A NEWTON-TYPE METHOD OF ORDER THREEIoannis K. Argyros, Said Hilout한국수학교육학회 · 이론수학과 교직수학2010 · 제17권 제1호EXPANDING THE CONVERGENCE DOMAIN FOR CHUN-STANICA-NETA FAMILY OF THIRD ORDER METHODS IN BANACH SPACESAngel Alberto Magrenan, Ioannis Konstantinos Argyros, Santhosh George대한수학회 · 대한수학회지2015 · 제52권 제1호CONCERNING THE RADII OF CONVERGENCE FOR ACERTAIN CLASS OF NEWTON-LIKE METHODSIoannis K. Argyros한국수학교육학회 · 이론수학과 교직수학2008 · 제15권 제1호ON THE RADIUS OF CONVERGENCE OF SOME NEWTON{TYPE METHODS IN BANACH SPACESIoannis K. Argyros, Said Hilout한국수학교육학회 · 이론수학과 교직수학2011 · 제18권 제3호

이 간행물의 다른 논문 (20건)

Large time behavior for the degenerate compressible Navier-Stokes equations with damping권영삼pp. 555-561Approximation properties of pairs of subspaces이근영pp. 563-568On cliques and Lagrangians of hypergraphsQingsong Tang, Xiangde Zhang, Cheng Zhaopp. 569-583Biisometric operators and biorthogonal sequencesCarlos Kubrusly, Nhan Levanpp. 585-596A note on meromorphic solutions of complex differential-difference equationsXiao-Guang Qi, Lian-Zhong Yangpp. 597-607
원문 보기