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Improved Convergence Analysis of Gauss-Newton-Secant Method for Solving Nonlinear Least Squares Problems

Author

Listed:
  • Ioannis Argyros

    (Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA)

  • Stepan Shakhno

    (Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine)

  • Yurii Shunkin

    (Department of Theory of Optimal Processes, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine)

Abstract

We study an iterative differential-difference method for solving nonlinear least squares problems, which uses, instead of the Jacobian, the sum of derivative of differentiable parts of operator and divided difference of nondifferentiable parts. Moreover, we introduce a method that uses the derivative of differentiable parts instead of the Jacobian. Results that establish the conditions of convergence, radius and the convergence order of the proposed methods in earlier work are presented. The numerical examples illustrate the theoretical results.

Suggested Citation

  • Ioannis Argyros & Stepan Shakhno & Yurii Shunkin, 2019. "Improved Convergence Analysis of Gauss-Newton-Secant Method for Solving Nonlinear Least Squares Problems," Mathematics, MDPI, vol. 7(1), pages 1-13, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:99-:d:198927
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