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Numerical solution of differential equations

Rosenbrock methods for stiff differential equations are a family of single-step methods for solving ordinary differential equations.¹² They are related to the implicit Runge–Kutta methods³ and are also known as Kaps–Rentrop methods.⁴

Search method

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.⁵ 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.⁶ The method often identifies such a ridge which, in many applications, leads to a solution.⁷

See also

• Rosenbrock function
• Adaptive coordinate descent

External links

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

References

1. H. H. Rosenbrock, "Some general implicit processes for the numerical solution of differential equations", The Computer Journal (1963) 5(4): 329-330 https://academic.oup.com/comjnl/article/5/4/329/316388 ↩

2. Press, WH; Teukolsky, SA; Vetterling, WT; Flannery, BP (2007). "Section 17.5.1. Rosenbrock Methods". Numerical Recipes: The Art of Scientific Computing (3rd ed.). New York: Cambridge University Press. ISBN 978-0-521-88068-8. 978-0-521-88068-8 ↩

3. "Archived copy" (PDF). Archived from the original (PDF) on 2013-10-29. Retrieved 2013-05-16.{{cite web}}: CS1 maint: archived copy as title (link) https://web.archive.org/web/20131029210710/http://www.cfm.brown.edu/people/jansh/page5/page10/page40/assets/Yu_Talk.pdf ↩

4. "Rosenbrock Methods". http://mathworld.wolfram.com/RosenbrockMethods.html ↩

5. H. H. Rosenbrock, "An Automatic Method for Finding the Greatest or Least Value of a Function", The Computer Journal (1960) 3(3): 175-184 ↩

6. Leader, Jeffery J. (2004). Numerical Analysis and Scientific Computation. Addison Wesley. ISBN 0-201-73499-0. 0-201-73499-0 ↩

7. Shoup, T., Mistree, F., Optimization methods: with applications for personal computers, 1987, Prentice Hall, pg. 120 [1] https://books.google.com/books?id=q0zvAAAAMAAJ&q=%22Rosenbrock+search%22&dq=%22Rosenbrock+search%22&hl=en ↩