Next Article in Journal
What Do a Longest Increasing Subsequence and a Longest Decreasing Subsequence Know about Each Other?
Previous Article in Journal
Exploring an Ensemble of Methods that Combines Fuzzy Cognitive Maps and Neural Networks in Solving the Time Series Prediction Problem of Gas Consumption in Greece
Article

Stability Analysis of Jacobian-Free Newton’s Iterative Method

1
Department of Mathematics, Faculty of Science, Razi University, 67149 Kermanshah, Iran
2
Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
*
Author to whom correspondence should be addressed.
Algorithms 2019, 12(11), 236; https://doi.org/10.3390/a12110236
Received: 3 October 2019 / Revised: 30 October 2019 / Accepted: 2 November 2019 / Published: 6 November 2019
It is well known that scalar iterative methods with derivatives are highly more stable than their derivative-free partners, understanding the term stability as a measure of the wideness of the set of converging initial estimations. In multivariate case, multidimensional dynamical analysis allows us to afford this task and it is made on different Jacobian-free variants of Newton’s method, whose estimations of the Jacobian matrix have increasing order. The respective basins of attraction and the number of fixed and critical points give us valuable information in this sense. View Full-Text
Keywords: nonlinear system of equations; iterative method; Jacobian-free scheme; basin of attraction nonlinear system of equations; iterative method; Jacobian-free scheme; basin of attraction
Show Figures

Figure 1

MDPI and ACS Style

Amiri, A.; Cordero, A.; Darvishi, M.T.; Torregrosa, J.R. Stability Analysis of Jacobian-Free Newton’s Iterative Method. Algorithms 2019, 12, 236. https://doi.org/10.3390/a12110236

AMA Style

Amiri A, Cordero A, Darvishi MT, Torregrosa JR. Stability Analysis of Jacobian-Free Newton’s Iterative Method. Algorithms. 2019; 12(11):236. https://doi.org/10.3390/a12110236

Chicago/Turabian Style

Amiri, Abdolreza, Alicia Cordero, Mohammad T. Darvishi, and Juan R. Torregrosa. 2019. "Stability Analysis of Jacobian-Free Newton’s Iterative Method" Algorithms 12, no. 11: 236. https://doi.org/10.3390/a12110236

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop