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Volume 22, Issue 3
Third Order Iterative Methods Without Using Second Fréchet Derivative

Sergio Amat, Sonia Busquier & Vicente Candela

J. Comp. Math., 22 (2004), pp. 341-346.

Published online: 2004-06

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  • Abstract

A modification of classical third order methods is proposed. The main advantage of these methods is that they do not need evaluate any second order Fréchet derivative. A convergence theorem in Banach spaces is analyzed. Finally, some preliminary numerical results are presented. 

  • Keywords

Nonlinear equations in Banach spaces, Third-order iterations, Divided difference.

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COPYRIGHT: © Global Science Press

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@Article{JCM-22-341, author = {Sergio Amat, Sonia Busquier and Vicente Candela }, title = {Third Order Iterative Methods Without Using Second Fréchet Derivative}, journal = {Journal of Computational Mathematics}, year = {2004}, volume = {22}, number = {3}, pages = {341--346}, abstract = {

A modification of classical third order methods is proposed. The main advantage of these methods is that they do not need evaluate any second order Fréchet derivative. A convergence theorem in Banach spaces is analyzed. Finally, some preliminary numerical results are presented. 

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8854.html} }
TY - JOUR T1 - Third Order Iterative Methods Without Using Second Fréchet Derivative AU - Sergio Amat, Sonia Busquier & Vicente Candela JO - Journal of Computational Mathematics VL - 3 SP - 341 EP - 346 PY - 2004 DA - 2004/06 SN - 22 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8854.html KW - Nonlinear equations in Banach spaces, Third-order iterations, Divided difference. AB -

A modification of classical third order methods is proposed. The main advantage of these methods is that they do not need evaluate any second order Fréchet derivative. A convergence theorem in Banach spaces is analyzed. Finally, some preliminary numerical results are presented. 

Sergio Amat, Sonia Busquier and Vicente Candela . (2004). Third Order Iterative Methods Without Using Second Fréchet Derivative. Journal of Computational Mathematics. 22 (3). 341-346. doi:
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