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Semilocal Convergence with R-Order Three Theorems for the Chebyshev Method and Its Modifications

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Optimization, Simulation, and Control

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 76))

Abstract

In this chapter we consider some modifications of the Chebyshev method that are free from second derivative and prove semilocal convergence theorems for these modifications as well as for the Chebyshev method. These two modifications can be considered as a generalization of some well-known iterative methods.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, National University of Mongolia, Ulaanbaatar, Mongolia

    Zhanlav Tugal & Khongorzul Dorjgotov

Authors
  1. Zhanlav Tugal
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  2. Khongorzul Dorjgotov
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Corresponding author

Correspondence to Zhanlav Tugal .

Editor information

Editors and Affiliations

  1. , Institute of Mathematics, National University of Mongolia, University Street 1, Ulaanbaatar, 210646, Erdenet, Mongolia

    Altannar Chinchuluun

  2. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  3. The School of Economic Studies, Dept.of Mathematics & Computer Science, National University of Mongolia, Ulaanbaatar, 210646, Mongolia

    Rentsen Enkhbat

  4. , Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom

    E. N. Pistikopoulos

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Tugal, Z., Dorjgotov, K. (2013). Semilocal Convergence with R-Order Three Theorems for the Chebyshev Method and Its Modifications. In: Chinchuluun, A., Pardalos, P., Enkhbat, R., Pistikopoulos, E. (eds) Optimization, Simulation, and Control. Springer Optimization and Its Applications, vol 76. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5131-0_21

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