Rosenbrock methods#Numerical solution of differential equations

Rosenbrock methods for stiff differential equations are a family of single-step methods for solving ordinary differential equations.H. H. Rosenbrock, [https://academic.oup.com/comjnl/article/5/4/329/316388 "Some general implicit processes for the numerical solution of differential equations"], The Computer Journal (1963) 5(4): 329-330{{Cite book | last1=Press | first1=WH | author-link1=William H. Press| last2=Teukolsky | first2=SA | author-link2=Saul Teukolsky|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=Section 17.5.1. Rosenbrock Methods | chapter-url=http://apps.nrbook.com/empanel/index.html#pg=935}} They are related to the implicit Runge–Kutta methods{{Cite web |url=http://www.cfm.brown.edu/people/jansh/page5/page10/page40/assets/Yu_Talk.pdf |title=Archived copy |access-date=2013-05-16 |archive-date=2013-10-29 |archive-url=https://web.archive.org/web/20131029210710/http://www.cfm.brown.edu/people/jansh/page5/page10/page40/assets/Yu_Talk.pdf |url-status=dead }} and are also known as Kaps–Rentrop methods.{{Cite web|url=http://mathworld.wolfram.com/RosenbrockMethods.html|title=Rosenbrock Methods}}

Rosenbrock search is a numerical optimization algorithm applicable to optimization problems in which the objective function is inexpensive to compute and the derivative either does not exist or cannot be computed efficiently.H. H. Rosenbrock, "An Automatic Method for Finding the Greatest or Least Value of a Function", The Computer Journal (1960) 3(3): 175-184 The idea of Rosenbrock search is also used to initialize some root-finding routines, such as fzero (based on Brent's method) in Matlab. Rosenbrock search is a form of derivative-free search but may perform better on functions with sharp ridges.{{cite book |last=Leader |first=Jeffery J. | author-link=Jeffery J. Leader| title=Numerical Analysis and Scientific Computation |year=2004 |publisher=Addison Wesley |isbn= 0-201-73499-0}} The method often identifies such a ridge which, in many applications, leads to a solution.Shoup, T., Mistree, F., Optimization methods: with applications for personal computers, 1987, Prentice Hall, pg. 120 [https://books.google.com/books?id=q0zvAAAAMAAJ&q=%22Rosenbrock+search%22&dq=%22Rosenbrock+search%22&hl=en]

• Rosenbrock function
• Adaptive coordinate descent

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• http://www.applied-mathematics.net/optimization/rosenbrock.html

{{Optimization algorithms}}

Category:Optimization algorithms and methods