Khác biệt giữa các bản “Phương pháp Newton”

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Trong [[giải tích số]], '''phương pháp Newton''' (còn được gọi là '''phương pháp Newton–Raphson'''), đặt tên theo [[Isaac Newton]] và Joseph Raphson, là một phương pháp tìm [[nghiệm]] xấp xỉ gần đúng của một [[hàm số]] có tham số thực.
: <math>x : f(x) = 0 \,.</math>
Phương pháp Newton–Raphson với một biến được thực hiện như sau
* Kendall E. Atkinson, ''An Introduction to Numerical Analysis'', (1989) John Wiley & Sons, Inc, {{isbn|0-471-62489-6}}
* Tjalling J. Ypma, Historical development of the Newton-Raphson method, ''SIAM Review'' '''37''' (4), 531–551, 1995. {{doi|10.1137/1037125}}.
* {{citechú bookthích sách|last1=Bonnans|first1=J.&nbsp;Frédéric|last2=Gilbert|first2=J.&nbsp;Charles|last3=Lemaréchal|first3=Claude| authorlink3=Claude Lemaréchal|last4=Sagastizábal|first4=Claudia&nbsp;A.|title=Numerical optimization: Theoretical and practical aspects|url=|edition=Second revised ed. of translation of 1997 <!-- ''Optimisation numérique: Aspects théoriques et pratiques'' --> French| series=Universitext|publisher=Springer-Verlag|location=Berlin|year=2006|pages=xiv+490|isbn=3-540-35445-X|doi=10.1007/978-3-540-35447-5|mr=2265882}}
* P. Deuflhard, ''Newton Methods for Nonlinear Problems. Affine Invariance and Adaptive Algorithms.'' Springer Series in Computational Mathematics, Vol. 35. Springer, Berlin, 2004. {{isbn|3-540-21099-7}}.
* C. T. Kelley, ''Solving Nonlinear Equations with Newton's Method'', no 1 in Fundamentals of Algorithms, SIAM, 2003. {{isbn|0-89871-546-6}}.
* J. M. Ortega, W. C. Rheinboldt, ''Iterative Solution of Nonlinear Equations in Several Variables.'' Classics in Applied Mathematics, SIAM, 2000. {{isbn|0-89871-461-3}}.
*{{Citechú bookthích sách | last1=Press | first1=WH | last2=Teukolsky | first2=SA | last3=Vetterling | first3=WT | last4=Flannery | first4=BP | year=2007 | title=Numerical Recipes: The Art of Scientific Computing | edition=3rd | publisher=Cambridge University Press | publication-place=New York | isbn=978-0-521-88068-8 | chapter=Chapter 9. Root Finding and Nonlinear Sets of Equations Importance Sampling | chapter-url=}}. See especially Sections [ 9.4], [ 9.6], and [ 9.7].
* [[Endre Süli]] and David Mayers, ''An Introduction to Numerical Analysis'', Cambridge University Press, 2003. {{isbn|0-521-00794-1}}.
* {{Cite document | last1=Kaw | first1=Autar | last2=Kalu | first2=Egwu | year=2008 | title=Numerical Methods with Applications | edition=1st | publisher= | postscript=<!-- Bot inserted parameter. Either remove it; or change its value to "." for the cite to end in a ".", as necessary. -->{{inconsistent citations}}}}.
* Gil, A., Segura, J., & Temme, N. M. , ''Numerical methods for special functions'' (2007) Society for Industrial and Applied Mathematics.
==Tham khảo==
{{tham khảo}}