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Impact of Interchange of Coefficients on Various Fixed Point Iterative Schemes

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Proceedings of International Conference on Trends in Computational and Cognitive Engineering

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1169))

Abstract

Sometimes the coefficients included in the fixed point iteration methods have a crucial impact in estimating the convergence rate of these iteration procedures. To prove this fact, a comparison among Modified-Mann (MM), Modified-Noor (MN) and Modified-Ishikawa (MI) iterative procedures have been done theoretically, numerically, as well as graphically. Here, the concept of interchange of coefficients involved in the iteration schemes is applied on Modified-Mann (MM), Modified-Noor (MN) and Modified-Ishikawa (MI) iterative procedures. Further, we analyze the speed of convergence of these iteration methods and finally a better result is obtained in the form of speed of convergence of the Modified-Ishikawa (MI) iteration but it remains stable in the Modified-Mann (MN) and Modified-Noor (MN) iterations. The convergence behaviour of these iterative processes for a given function is also plotted graphically to elaborate on the analysis part of these iteration schemes.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University Institute of Sciences, Chandigarh University, Gharuan, Mohali, 140413, Punjab, India

    Naveen Kumar & Surjeet Singh Chauhan (Gonder)

Authors
  1. Naveen Kumar
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  2. Surjeet Singh Chauhan (Gonder)
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Corresponding author

Correspondence to Naveen Kumar .

Editor information

Editors and Affiliations

  1. Central University of Haryana, Mahendergarh, India

    Phool Singh

  2. Central University of Haryana, Mahendergarh, India

    Rajesh Kumar Gupta

  3. Amity School of Applied Sciences, Amity School of Engineering and Technology (ASET), Jaipur, Rajasthan, India

    Kanad Ray

  4. Surface Characterization Group, National Institute for Materials Science (NIMS), Tsukuba, Ibaraki, Japan

    Anirban Bandyopadhyay

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Kumar, N., Chauhan (Gonder), S.S. (2021). Impact of Interchange of Coefficients on Various Fixed Point Iterative Schemes. In: Singh, P., Gupta, R.K., Ray, K., Bandyopadhyay, A. (eds) Proceedings of International Conference on Trends in Computational and Cognitive Engineering. Advances in Intelligent Systems and Computing, vol 1169. Springer, Singapore. https://doi.org/10.1007/978-981-15-5414-8_4

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