Rosenbrock methods
Rosenbrock methods refers to either of two distinct ideas in numerical computation, both named for Howard H. Rosenbrock.
Numerical solution of differential equations
[edit | edit source]Rosenbrock 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
[edit | edit source]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
[edit | edit source]References
[edit | edit source]- ^ H. H. Rosenbrock, "Some general implicit processes for the numerical solution of differential equations", The Computer Journal (1963) 5(4): 329-330
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- ^ H. H. Rosenbrock, "An Automatic Method for Finding the Greatest or Least Value of a Function", The Computer Journal (1960) 3(3): 175-184
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- ^ Shoup, T., Mistree, F., Optimization methods: with applications for personal computers, 1987, Prentice Hall, pg. 120 [1]
