Rosenbrock methods refers to either of two distinct ideas in
numerical computation
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods t ...
, both named for
Howard H. Rosenbrock.
Numerical solution of differential equations
Rosenbrock methods for
stiff differential equations are a family of single-step methods for solving
ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable (mathematics), variable. As with any other DE, its unknown(s) consists of one (or more) Function (mathematic ...
s. They are related to the
implicit Runge–Kutta methods
Implicit may refer to:
Mathematics
* Implicit function
* Implicit function theorem
* Implicit curve
* Implicit surface
* Implicit differential equation
Other uses
* Implicit assumption, in logic
* Implicit-association test, in social psychology ...
and are also known as Kaps–Rentrop methods.
Search method
Rosenbrock search is a
numerical optimization algorithm applicable to optimization problems in which the
objective function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cost ...
is inexpensive to compute and the derivative either does not exist or cannot be computed efficiently. The idea of Rosenbrock search is also used to initialize some
root-finding routines, such as fzero (based on
Brent's method
In numerical analysis, Brent's method is a hybrid root-finding algorithm combining the bisection method, the secant method and inverse quadratic interpolation. It has the reliability of bisection but it can be as quick as some of the less-reliab ...
) in
Matlab
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementat ...
. Rosenbrock search is a form of
derivative-free search but may perform better on functions with sharp ridges. 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. 12]
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See also
* Rosenbrock function
* Adaptive coordinate descent
References
External links
* http://www.applied-mathematics.net/optimization/rosenbrock.html
{{Optimization algorithms
Optimization algorithms and methods