نیوتون رویه‌سی اوچون قایناغا باخین

'''نیوتون رویه‌سی''' (Newton's method) یادا نیوتون-رافسون اوصولو. بیر تابع ده ریشه تاپماق القوریتمدیر. بیر تابع ده باشدا تابع ریشه‌سین ظن ایله تاپیب و سونرا فورمولدا اونو تقریبی اله گتیریر. ان یاخین [[سایی]] تابع ریشه‌سی و [[کؤک]]ودور.

:<math>x_{1} = x_0 - \frac{f(x_0)}{f'(x_0)} \,.</math>


<!-- [[Image:newton iteration.svg|alt=Illustration of Newton's method|thumb|right|300px|An illustration of one iteration of Newton's method (the function {{mvar|f}} is shown in blue and the tangent line is in red). We see that {{math|''x''<sub>''n'' + 1</sub>}} is a better approximation than {{math|''x''<sub>''n''</sub>}} for the root {{math|''x''}} of the function {{math|''f''}}.]] -->
[[Image:NewtonIteration Ani.gif|alt=Illustration of Newton's method|thumb|right|300px|The function {{mvar|f}} is shown in blue and the tangent line is in red. We see that {{math|''x''<sub>''n'' + 1</sub>}} is a better approximation than {{math|''x''<sub>''n''</sub>}} for the root {{mvar|x}} of the function {{mvar|f}}.]] 

== قایناقلار == 
{{قایناق|colwidth=35em|refs=

<ref name="Colli and Girault, 2017" >{{Cite journal
  |title=Compact and General Strategy for Solving Current and Potential Distribution in Electrochemical Cells Composed of Massive Monopolar and Bipolar Electrodes
  |first1=A. N.  |last1=Colli
  |first2=H. H.  |last2=Girault
  |journal=Journal of the Electrochemical Society
  |volume=164  |issue=11
  |pages=E3465-E3472
  |date=June 2017
  |doi=10.1149/2.0471711jes  |hdl=11336/68067
  |hdl-access=free
  }}</ref>

}}

==References==
* {{cite book |last1=Gil |first1=A. |last2=Segura |first2=J. |last3=Temme |first3=N. M. |url=https://www.researchgate.net/publication/220693008 |title=Numerical methods for special functions |isbn=978-0-89871-634-4 |date=2007 |publisher=Society for Industrial and Applied Mathematics |ref=harv}}
* {{cite book |author1-link=Endre Süli |first1=Endre |last1=Süli |first2=David |last2=Mayers |title=An Introduction to Numerical Analysis |publisher=Cambridge University Press |date=2003 |isbn=0-521-00794-1 |ref=harv}}

==آرتیق اوخو==
* 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}}.
* {{cite book|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.|author4-link= Claudia Sagastizábal |title=Numerical optimization: Theoretical and practical aspects|url=https://www.springer.com/mathematics/applications/book/978-3-540-35445-1|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}}.
*{{Cite book |last1=Press |first1=W. H. |last2=Teukolsky |first2=S. A. |last3=Vetterling |first3=W. T. |last4=Flannery |first4=B. P. |year=2007 |title=Numerical Recipes: The Art of Scientific Computing |edition=3rd |publisher=Cambridge University Press |location=New York |isbn=978-0-521-88068-8 |chapter=Chapter 9. Root Finding and Nonlinear Sets of Equations Importance Sampling |chapter-url=http://apps.nrbook.com/empanel/index.html#pg=442 |access-date=2020-05-01 |archive-date=2011-08-11 |archive-url=https://web.archive.org/web/20110811154417/http://apps.nrbook.com/empanel/index.html#pg=442 |url-status=dead }}. See especially Sections [http://apps.nrbook.com/empanel/index.html#pg=456 9.4] {{Webarchive|url=https://web.archive.org/web/20110811154417/http://apps.nrbook.com/empanel/index.html#pg=456 |date=2011-08-11 }}, [http://apps.nrbook.com/empanel/index.html#pg=473 9.6] {{Webarchive|url=https://web.archive.org/web/20110811154417/http://apps.nrbook.com/empanel/index.html#pg=473 |date=2011-08-11 }}, and [http://apps.nrbook.com/empanel/index.html#pg=477 9.7] {{Webarchive|url=https://web.archive.org/web/20110811154417/http://apps.nrbook.com/empanel/index.html#pg=477 |date=2011-08-11 }}.
* {{cite book |first=Mordecai |last=Avriel |title=Nonlinear Programming: Analysis and Methods |url=https://archive.org/details/nonlinearprogram0000avri |location= |publisher=Prentice Hall |year=1976 |isbn=0-13-623603-0 |pages=[https://archive.org/details/nonlinearprogram0000avri/page/216 216]–221 }}

==ائشیک باغلانتیلار==
{{آمبار بؤلمه|Newton Method}}
{{Wikibooks category|Newton's method}}
* {{springer|title=Newton method|id=p/n066560}}
*{{MathWorld|title=Newton's Method|urlname=NewtonsMethod}}
*[http://en.citizendium.org/wiki/Newton%27s_method Newton's method, Citizendium.]
*[https://web.archive.org/web/20190524083302/http://mathfaculty.fullerton.edu/mathews/n2003/NewtonAccelerateMod.html Mathews, J., The Accelerated and Modified Newton Methods, Course notes.]
*[http://www.ece.mcmaster.ca/~xwu/part2.pdf Wu, X., Roots of Equations, Course notes.]

{{Isaac Newton}}
{{Optimization algorithms}}
{{Root-finding algorithms}}
{{Authority control}}

[[بؤلمه:فیزیک]]
[[بؤلمه:سایی]]