Gauss--Newton--Kurchatov method for the solution of non-linear least-square problems using ω-condition
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Naveen Chandra Bhagat
Abstract
We propose to study the convergence of an iterative method used for solving non-linear least-square problems having differentiable as well as non-differentiable functions. We use the ω-condition on both first order divided difference of non-differentiable part and first order derivative of differentiable part to establish the condition for convergence of the method. We also present some numerical experiments as test beds for the proposed method. In all the numerical examples, we have compared our results with a well-known Gauss–Newton–Potra method and shown that our convergence analysis gives better error bounds.
References
[1] I. K. Argyros, Convergence and Applications of Newton-Type Iterations, Springer, New York, 2008. Suche in Google Scholar
[2] I. K. Argyros, S. Shakhno and Y. V. Shunkin, Improved convergence analysis of Gauss–Newton–Secant method for solving nonlinear least squares problems, Mathematics 7 (2019), no. 1, Paper No. 99. 10.3390/math7010099Suche in Google Scholar
[3] I. K. Argyros, D. Sharma and S. K. Parhi, On the local convergence of Weerakoon–Fernando method with ω continuity condition in Banach spaces, SeMA J. 77 (2020), no. 3, 291–304. 10.1007/s40324-020-00217-ySuche in Google Scholar
[4] J. E. Dennis, Jr. and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Class. Appl. Math. 16, Society for Industrial and Applied Mathematics, Philadelphia, 1996. 10.1137/1.9781611971200Suche in Google Scholar
[5] H. Kumar and P. K. Parida, On semilocal convergence of two step Kurchatov method, Int. J. Comput. Math. 96 (2019), no. 8, 1548–1566. 10.1080/00207160.2018.1428741Suche in Google Scholar
[6] A. A. Magreñán and I. K. Argyros, A Contemporary Study of Iterative Methods. Convergence, Dynamics and Applications, Academic Press, London, 2018. 10.1016/B978-0-12-809214-9.00023-1Suche in Google Scholar
[7] J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 1970. Suche in Google Scholar
[8] H. Ren, I. K. Argyros and S. Hilout, A derivative free iterative method for solving least squares problems, Numer. Algorithms 58 (2011), no. 4, 555–571. 10.1007/s11075-011-9470-9Suche in Google Scholar
[9] S. M. Shakhno, Gauss–Newton–Kurchatov method for the solution of nonlinear least-squares problems, J. Math. Sci. (N. Y.) 247 (2020), no. 1, 58–72. 10.1007/s10958-020-04789-ySuche in Google Scholar
[10]
S. M. Shakhno and O. P. Gnatyshyn,
On an iterative algorithm of order
[11] S. M. Shakhno and Y. Shunkin, One combined method for solving nonlinear least squares problems, Bull. Lviv Univ. Ser. Appl. Math. Inform. 25 (2017), 38–48. 10.15330/ms.48.1.97-107Suche in Google Scholar
[12] S. M. Shakhno and G. P. Yarmola, A two-point method for solving nonlinear equations with a nondifferentiable operator, Mat. Stud. 36 (2011), no. 2, 213–220. Suche in Google Scholar
[13] S. M. Shakhno, H. P. Yarmola and Y. V. Shunkin, Convergence analysis of the Gauss–Newton–Potra method for nonlinear least squares problems, Mat. Stud. 50 (2018), no. 2, 211–221. 10.15330/ms.50.2.211-221Suche in Google Scholar
[14] D. Sharma, S. K. Parhi and S. K. Sunanda, Convergence of Traub’s iteration under ω continuity condition in Banach spaces, Russian Math. 65 (2021), 52–68. 10.3103/S1066369X21090073Suche in Google Scholar
© 2023 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- On left and right Browder elements in Banach algebra relative to a bounded homomorphism
- Uniform excess of g-frames
- On normal partial isometries
- Gauss--Newton--Kurchatov method for the solution of non-linear least-square problems using ω-condition
- Maps preserving the bi-skew Jordan product on factor von Neumann algebras
- Boundary contact problems with regard to friction of couple-stress viscoelasticity for inhomogeneous anisotropic bodies (quasi-static cases)
- On uniform statistical convergence
- Approximate solution of the optimal control problem for non-linear differential inclusion on the semi-axes
- Energy-based localization of positive solutions for stationary Kirchhoff-type equations and systems
- e-reversibility of rings via quasinilpotents
- Weighted generalized Moore–Penrose inverse
- On two extensions of the annihilating-ideal graph of commutative rings
- Umbral treatment and lacunary generating function for Hermite polynomials
- A generalization of the canonical commutation relation and Heisenberg uncertainty principle for the orbital operators
Artikel in diesem Heft
- Frontmatter
- On left and right Browder elements in Banach algebra relative to a bounded homomorphism
- Uniform excess of g-frames
- On normal partial isometries
- Gauss--Newton--Kurchatov method for the solution of non-linear least-square problems using ω-condition
- Maps preserving the bi-skew Jordan product on factor von Neumann algebras
- Boundary contact problems with regard to friction of couple-stress viscoelasticity for inhomogeneous anisotropic bodies (quasi-static cases)
- On uniform statistical convergence
- Approximate solution of the optimal control problem for non-linear differential inclusion on the semi-axes
- Energy-based localization of positive solutions for stationary Kirchhoff-type equations and systems
- e-reversibility of rings via quasinilpotents
- Weighted generalized Moore–Penrose inverse
- On two extensions of the annihilating-ideal graph of commutative rings
- Umbral treatment and lacunary generating function for Hermite polynomials
- A generalization of the canonical commutation relation and Heisenberg uncertainty principle for the orbital operators
