Research Article

Local convergence for composite Chebyshev-type methods

Volume: 1 Number: 1 September 30, 2018
İoannis K Argyros , Santhosh George *
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Communications in Advanced Mathematical Sciences Cover Communications in Advanced Mathematical Sciences
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Local convergence for composite Chebyshev-type methods

Abstract

We replace Chebyshev's method for solving equations requiring the second derivative by a Chebyshev-type second derivative free method. The local convergence analysis of the new method is provided using hypotheses only on the first derivative in contrast to the Chebyshev method using hypotheses on the second derivative. This way we extend the applicability of the method. Numerical examples are also used to test the convergence criteria and to obtain error bounds and also the radius of convergence.

Keywords

Chebyshev method,Newton method,Fr\'echet derivative,Local convergence,Divided differences

References

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  8. [8] H. T. Kung, J. F. Traub, Optimal order of one-point and multipoint iteration, J. ACM 21, (1974), 643-651.
  9. [9] A. A. Magrenan, Different anomalies in a Jarratt family of iterative root finding methods, Appl. Math. Comput. 233, (2014), 29-38.
  10. [10] A. A. Magren´an, A new tool to study real dynamics: The convergence plane, Appl. Math. Comput. 248, (2014), 29-38.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

İoannis K Argyros This is me
United States

Santhosh George * This is me
India

Publication Date

September 30, 2018

Submission Date

July 6, 2018

Acceptance Date

August 17, 2018

Published in Issue

Year 2018 Volume: 1 Number: 1

DOI

https://doi.org/10.33434/cams.441220

IZ

https://izlik.org/JA98HL26XW

Cite

RIS / Bibtex
APA
Argyros, İ. K., & George, S. (2018). Local convergence for composite Chebyshev-type methods. Communications in Advanced Mathematical Sciences, 1(1), 84-90. https://doi.org/10.33434/cams.441220
AMA
1.Argyros İK, George S. Local convergence for composite Chebyshev-type methods. Communications in Advanced Mathematical Sciences. 2018;1(1):84-90. doi:10.33434/cams.441220
Chicago
Argyros, İoannis K, and Santhosh George. 2018. “Local Convergence for Composite Chebyshev-Type Methods”. Communications in Advanced Mathematical Sciences 1 (1): 84-90. https://doi.org/10.33434/cams.441220.
EndNote
Argyros İK, George S (September 1, 2018) Local convergence for composite Chebyshev-type methods. Communications in Advanced Mathematical Sciences 1 1 84–90.
IEEE
[1]İ. K. Argyros and S. George, “Local convergence for composite Chebyshev-type methods”, Communications in Advanced Mathematical Sciences, vol. 1, no. 1, pp. 84–90, Sept. 2018, doi: 10.33434/cams.441220.
ISNAD
Argyros, İoannis K - George, Santhosh. “Local Convergence for Composite Chebyshev-Type Methods”. Communications in Advanced Mathematical Sciences 1/1 (September 1, 2018): 84-90. https://doi.org/10.33434/cams.441220.
JAMA
1.Argyros İK, George S. Local convergence for composite Chebyshev-type methods. Communications in Advanced Mathematical Sciences. 2018;1:84–90.
MLA
Argyros, İoannis K, and Santhosh George. “Local Convergence for Composite Chebyshev-Type Methods”. Communications in Advanced Mathematical Sciences, vol. 1, no. 1, Sept. 2018, pp. 84-90, doi:10.33434/cams.441220.
Vancouver
1.İoannis K Argyros, Santhosh George. Local convergence for composite Chebyshev-type methods. Communications in Advanced Mathematical Sciences. 2018 Sep. 1;1(1):84-90. doi:10.33434/cams.441220

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