Rosenbrock methods

From Wikipedia, the free encyclopedia
Jump to: navigation, search

Rosenbrock methods refers to either of two distinct ideas in numerical computation, both named for Howard H. Rosenbrock.

Numerical solution of differential equations[edit]

Rosenbrock methods for stiff differential equations are a family of multistep methods for solving ordinary differential equations that contain a wide range of characteristic timescales.[1][2] They are related to the implicit Runge-Kutta methods[3] and are also known as Kaps-Rentrop methods.[4]

Search method[edit]

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 derivate-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[edit]

References[edit]

  1. ^ H. H. Rosenbrock, "Some general implicit processes for the numerical solution of differential equations", The Computer Journal (1963) 5(4): 329-330
  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. 
  3. ^ http://www.cfm.brown.edu/people/jansh/page5/page10/page40/assets/Yu_Talk.pdf
  4. ^ 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. 
  7. ^ Shoup, T., Mistree, F., Optimization methods: with applications for personal computers, 1987, Prentice Hall, pg. 120 [1]

External links[edit]