Skip to main content
SpringerLink
Log in

Ball Convergence of Multipoint Methods for Non-linear Systems

  • Conference paper
  • First Online:
Computational Sciences - Modelling, Computing and Soft Computing (CSMCS 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1345))

  • 218 Accesses

Abstract

We study Multipoint methods using only the first derivative. Earlier studies use higher than three order derivatives not on the methods. Moreover Lipschitz constants are used to find error estimates not presented in earlier papers. Numerical examples complete this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Argyros, I.K.: Computational Theory of Iterative Solvers Series: Studies in Computational Mathematics. In: Chui, C.K., Wuytack, L., et al. (eds.) Elsevier Publ. Co., New York, U.S.A (2007)

    Google Scholar 

  2. Argyros, I.K., Magréñan, A.A.: A Contemporary Study of Iterative Methods, Elsevier. Academic Press), New York (2018)

    MATH  Google Scholar 

  3. Argyros, I.K., Magréñan, A.A.: Iterative Methods and their Dynamics with Applications. CRC Press, New York, USA (2017)

    Book  Google Scholar 

  4. Argyros, I.K., George, S.: Mathematical Modeling for the Solution of Equations and Systems of Equations with Applications. Nova Publishers, New York, Volume-III (2019)

    Google Scholar 

  5. Cordero, A., Torregrosa, J.R., Vassileva, M.P.: Increasing the order of convergence of iterative scheme for solving non-linear systems. J. Comput. Appl. Math. 2012,(2012). https://doi.org/10.1016/j.cam.2012.11.024

  6. Cordero, A., Hueso, J.L., Martinez, E., Torregrosa, J.: A modified Newton-Jarratta’s composition. Numer. Algor. 55, 87–99 (2010)

    Article  Google Scholar 

  7. Ezquerro, J.A., Hernández, M.A.: On the R-order of the Halley method. J. Math. Anal. Appl. 303, 591–601 (2005)

    Article  MathSciNet  Google Scholar 

  8. Kantorovich, L.V., Akilov, G.P.: Functional Analysis. Pergamon Press, Oxford (1982)

    MATH  Google Scholar 

  9. Parhi, S.K., Gupta, D.K.: Recurrence relations for a Newton-like method in Banach spaces. J. Comput. Appl. Math. 206(2), 873–887 (2007)

    Article  MathSciNet  Google Scholar 

  10. Potra, F.A., Ptak, V.: Nondiscrete induction and iterative processes. Pitman Advanced Publishing Program 103 (1984)

    Google Scholar 

  11. Ren, H., Wu, Q., Bi, W.: New variants of Jarratt method with sixth-order convergence. Numer. Algor. 52(4), 585–603 (2009)

    Article  MathSciNet  Google Scholar 

  12. Rheinboldt, W.C.: An adaptive continuation process for solving systems of nonlinear equations, Mathematical models and numerical methods. In: Tikhonov, A.N., et al. (eds.) 3(19), Banach Center, Warsaw Poland, pp. 129–142 (1978)

    Google Scholar 

  13. Rostamy, D., Bakhtiari, P.: New efficient multipoint iterative method for solving nonlinear systems. Appl. Math. Comput. 266, 350–356 (2015)

    MathSciNet  MATH  Google Scholar 

  14. Sharma, J.R., Arora, H.: Efficient Jarratt-like methods for solving systems of nonlinear equations. Calcolo 51(1), 193–210 (2013). https://doi.org/10.1007/s10092-013-0097-1

    Article  MathSciNet  MATH  Google Scholar 

  15. Sharma, J.R., Guha, R.K., Sharma, R.: An efficient fourth order weighted-Newton method for systems of nonlinear equations. Numer. Algor. 62, 307–323 (2013)

    Article  MathSciNet  Google Scholar 

  16. Sharma, J.R., Arora, H.: Improved Newton-like solvers for solving systems of nonlinear equations. SEMA J. 74(2), 147–163 (2017)

    Article  MathSciNet  Google Scholar 

  17. Soleymani, F., Lotfi, T., Bakhtiari, P.: A multi-step class of iterative methods for nonlinear systems. Optimization Letters 8(3), 1001–1015 (2013). https://doi.org/10.1007/s11590-013-0617-6

    Article  MathSciNet  MATH  Google Scholar 

  18. Traub, J.F.: Iterative Methods for the Solution of equations. Prentice hall, New York (1964)

    MATH  Google Scholar 

  19. Wang, X., Kou, J.: Semilocal convergence of a modified multi-point Jarratt method in Banach spaces under general continuity conditions. Numer. Algor. 60, 369–390 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore, 575 025, India

    Santhosh George

  3. Department of Mathematics, Manipal Institute of Technology, Manipal, Karnataka, 576104, India

    Shobha M. Erappa

Authors
  1. Ioannis K. Argyros
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Santhosh George
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shobha M. Erappa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shobha M. Erappa .

Editor information

Editors and Affiliations

  1. National Institute of Technology Calicut, Kozhikode, Kerala, India

    Ashish Awasthi

  2. National Institute of Technology Calicut, Kozhikode, Kerala, India

    Sunil Jacob John

  3. National Institute of Technology Calicut, Kozhikode, Kerala, India

    Satyananda Panda

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Argyros, I.K., George, S., Erappa, S.M. (2021). Ball Convergence of Multipoint Methods for Non-linear Systems. In: Awasthi, A., John, S.J., Panda, S. (eds) Computational Sciences - Modelling, Computing and Soft Computing. CSMCS 2020. Communications in Computer and Information Science, vol 1345. Springer, Singapore. https://doi.org/10.1007/978-981-16-4772-7_21

Download citation

  • DOI: https://doi.org/10.1007/978-981-16-4772-7_21

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-4771-0

  • Online ISBN: 978-981-16-4772-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation