Rosenbrock methods refers to either of two distinct ideas in numerical computation, both named for Howard H. Rosenbrock.
Numerical solution of differential equations
editRosenbrock methods for stiff differential equations are a family of single-step methods for solving ordinary differential equations.[1][2] They are related to the implicit Runge–Kutta methods[3] and are also known as Kaps–Rentrop methods.[4]
Search method
editRosenbrock 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
editReferences
edit- ^ H. H. Rosenbrock, "Some general implicit processes for the numerical solution of differential equations", The Computer Journal (1963) 5(4): 329-330
- ^ 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.
- ^ "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) - ^ "Rosenbrock Methods".
- ^ H. H. Rosenbrock, "An Automatic Method for Finding the Greatest or Least Value of a Function", The Computer Journal (1960) 3(3): 175-184
- ^ Leader, Jeffery J. (2004). Numerical Analysis and Scientific Computation. Addison Wesley. ISBN 0-201-73499-0.
- ^ Shoup, T., Mistree, F., Optimization methods: with applications for personal computers, 1987, Prentice Hall, pg. 120 [1]