Research Article
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Year 2022, , 452 - 458, 30.12.2022
https://doi.org/10.53006/rna.1138201

Abstract

References

  • 1. I.K. Argyros, S. Hailout, Computational methods in nonlinear analysis: efficient algorithms, fixed point theory and applications, World Scientific (2013).
  • 2. A. Cordero, A. Franques, J.R. Torregrosa, Chaos and convergence of a family generalizing homeier's method with damping parameters, Nonlinear Dynamics 85(3) (2016) 1939-1954.
  • 3. A. Cordero, M.A. Hernandez-Veron, N. Romero, J.R. Torregrosa, Semilocal Convergence by using recurrence relations for a fifth-order method in banach spaces, Journal of Computational and Applied Mathematics 273 (2015) 205-213.
  • 4. S. George, I.K. Argyros, K. Senapati, K. Kanagaraj, Local convergence analysis of two iterative methods, The Journal of Analysis (2022) 1-12.
  • 5. M. Grau-Sanchez, A. Grau, M. Noguera, On the computational efficiency index and some iterative methods for solving systems of nonlinear equations, Journal of Computational and Applied Mathematics 236(6) (2011) 1259-1266.
  • 6. H.H.H. Homeier, A modified newton method with cubic convergence: the multiverse case, Journal of Computational and Applied Mathematics 168(1) (2004) 161-169.
  • 7. P. Jarratt, Some fourth order multipoint iterative methods for solving equations, Mathematics of computation 20(95) (1966) 434-437.
  • 8. C.T. Kelley, Iterative methods for linear and nonlinear equations, SIAM (1995).
  • 9. J.M. Ortega, W.C. Rheinboldt, Iterative solution of nonlinear equations in several variables, SIAM (2000).
  • 10. A.M. Ostrowski, Solution of equations and system of equations, Pure and Applied Mathematics: A series of monographs and textbooks volume 9 (2016).
  • 11. L.I. Piscoran, D. Miclaus, A new steffensen homeier iterative method for solving nonlinear equations, Investigacion Operacional 40(1) (2019) 74-80.
  • 12. J.R. Sharma, P. Gupta, An efficient fifth order method for solving systems of nonlinear equations, Computers and Mathematics with Applications 67(3) (2014) 591-601.
  • 13. S. Singh, D.K. Gupta, E. Martinez, J.L Hueso, Semilocal convergence analysis of an iteration of order five using recurrence relations in banach spaces, Mediterranean Journal of Mathematics 13(6) (2016) 4219-4235.
  • 14. O.S. Solaiman, I. Hashim, An iterative scheme of arbitrary odd order and its basins of attraction for nonlinear systems, Computers, Materials and Continua Computers 66 (2021) 1427-1444.
  • 15. J.F. Traub, Iterative methods for the solution of equations, American Mathematical Society volume 312 (2013).
  • 16. S. Weerakoon, T.G.I. Fernando, A variant of newton's method with accelerated third-order convergence, Applied Mathematics Letters 13(8) (2000) 87-93.

On the convergence of the sixth order Homeier like method in Banach spaces

Year 2022, , 452 - 458, 30.12.2022
https://doi.org/10.53006/rna.1138201

Abstract

A sixth order Homeier-like method is introduced for approximating a solution of the non-linear equation in Banach space. Assumptions only on first and second derivatives are used to obtain a sixth order convergence. Our proof does not depend on Taylor series expansions as in the earlier studies for the similar methods.

References

  • 1. I.K. Argyros, S. Hailout, Computational methods in nonlinear analysis: efficient algorithms, fixed point theory and applications, World Scientific (2013).
  • 2. A. Cordero, A. Franques, J.R. Torregrosa, Chaos and convergence of a family generalizing homeier's method with damping parameters, Nonlinear Dynamics 85(3) (2016) 1939-1954.
  • 3. A. Cordero, M.A. Hernandez-Veron, N. Romero, J.R. Torregrosa, Semilocal Convergence by using recurrence relations for a fifth-order method in banach spaces, Journal of Computational and Applied Mathematics 273 (2015) 205-213.
  • 4. S. George, I.K. Argyros, K. Senapati, K. Kanagaraj, Local convergence analysis of two iterative methods, The Journal of Analysis (2022) 1-12.
  • 5. M. Grau-Sanchez, A. Grau, M. Noguera, On the computational efficiency index and some iterative methods for solving systems of nonlinear equations, Journal of Computational and Applied Mathematics 236(6) (2011) 1259-1266.
  • 6. H.H.H. Homeier, A modified newton method with cubic convergence: the multiverse case, Journal of Computational and Applied Mathematics 168(1) (2004) 161-169.
  • 7. P. Jarratt, Some fourth order multipoint iterative methods for solving equations, Mathematics of computation 20(95) (1966) 434-437.
  • 8. C.T. Kelley, Iterative methods for linear and nonlinear equations, SIAM (1995).
  • 9. J.M. Ortega, W.C. Rheinboldt, Iterative solution of nonlinear equations in several variables, SIAM (2000).
  • 10. A.M. Ostrowski, Solution of equations and system of equations, Pure and Applied Mathematics: A series of monographs and textbooks volume 9 (2016).
  • 11. L.I. Piscoran, D. Miclaus, A new steffensen homeier iterative method for solving nonlinear equations, Investigacion Operacional 40(1) (2019) 74-80.
  • 12. J.R. Sharma, P. Gupta, An efficient fifth order method for solving systems of nonlinear equations, Computers and Mathematics with Applications 67(3) (2014) 591-601.
  • 13. S. Singh, D.K. Gupta, E. Martinez, J.L Hueso, Semilocal convergence analysis of an iteration of order five using recurrence relations in banach spaces, Mediterranean Journal of Mathematics 13(6) (2016) 4219-4235.
  • 14. O.S. Solaiman, I. Hashim, An iterative scheme of arbitrary odd order and its basins of attraction for nonlinear systems, Computers, Materials and Continua Computers 66 (2021) 1427-1444.
  • 15. J.F. Traub, Iterative methods for the solution of equations, American Mathematical Society volume 312 (2013).
  • 16. S. Weerakoon, T.G.I. Fernando, A variant of newton's method with accelerated third-order convergence, Applied Mathematics Letters 13(8) (2000) 87-93.
There are 16 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Suma P B

M. E. Shobha

Santhosh George

Publication Date December 30, 2022
Published in Issue Year 2022

Cite

APA P B, S., Shobha, M. E., & George, S. (n.d.). On the convergence of the sixth order Homeier like method in Banach spaces. Results in Nonlinear Analysis, 5(4), 452-458. https://doi.org/10.53006/rna.1138201
AMA P B S, Shobha ME, George S. On the convergence of the sixth order Homeier like method in Banach spaces. RNA. 5(4):452-458. doi:10.53006/rna.1138201
Chicago P B, Suma, M. E. Shobha, and Santhosh George. “On the Convergence of the Sixth Order Homeier Like Method in Banach Spaces”. Results in Nonlinear Analysis 5, no. 4 n.d.: 452-58. https://doi.org/10.53006/rna.1138201.
EndNote P B S, Shobha ME, George S On the convergence of the sixth order Homeier like method in Banach spaces. Results in Nonlinear Analysis 5 4 452–458.
IEEE S. P B, M. E. Shobha, and S. George, “On the convergence of the sixth order Homeier like method in Banach spaces”, RNA, vol. 5, no. 4, pp. 452–458, doi: 10.53006/rna.1138201.
ISNAD P B, Suma et al. “On the Convergence of the Sixth Order Homeier Like Method in Banach Spaces”. Results in Nonlinear Analysis 5/4 (n.d.), 452-458. https://doi.org/10.53006/rna.1138201.
JAMA P B S, Shobha ME, George S. On the convergence of the sixth order Homeier like method in Banach spaces. RNA.;5:452–458.
MLA P B, Suma et al. “On the Convergence of the Sixth Order Homeier Like Method in Banach Spaces”. Results in Nonlinear Analysis, vol. 5, no. 4, pp. 452-8, doi:10.53006/rna.1138201.
Vancouver P B S, Shobha ME, George S. On the convergence of the sixth order Homeier like method in Banach spaces. RNA. 5(4):452-8.