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A note on the convergence of the secant method for simple and multiple roots

Author
Diez, P.
Type of activity
Journal article
Journal
Applied mathematics letters
Date of publication
2003-11
Volume
16
Number
8
First page
1211
Last page
1215
DOI
https://doi.org/10.1016/S0893-9659(03)90119-4 Open in new window
Repository
http://hdl.handle.net/2117/8459 Open in new window
Abstract
The secant method is one of the most popular methods for root finding. Standard text books in numerical analysis state that the secant method is super linear: the rate of convergence is set by the gold number. Never- theless, this property holds only for simple roots. If the multiplicity of the root is larger than one, the convergence of the secant method becomes linear. This communication includes a detailed analysis of the secant method when it is used to approximate multiple roots. Thus, a pr...
Citation
Díez, P. A note on the convergence of the secant method for simple and multiple roots. "Applied mathematics letters", Novembre 2003, vol. 16, núm. 8, p. 1211-1215.
Keywords
Asymptotic behavior, Convergence rate, Secant method
Group of research
LACÀN - Numerical Methods for Applied Sciences and Engineering

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