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Plot of the Rosenbrock function of two variables. Here a = 1 , b = 100 {\displaystyle a=1,b=100} , and the minimum value of zero is at ( 1 , 1 ) {\displaystyle (1,1)} . In mathematical optimization , the Rosenbrock function is a non- convex function , introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for ...
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]
An interpretation of the Rosenbrock System Matrix as a Linear Fractional Transformation can be found in. [4] One of the first applications of the Rosenbrock form was the development of an efficient computational method for Kalman decomposition , which is based on the pivot element method.
In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as convergence rate, precision, robustness and general performance.
In chemistry, a reaction coordinate [1] is an abstract one-dimensional coordinate chosen to represent progress along a reaction pathway. Where possible it is usually a geometric parameter that changes during the conversion of one or more molecular entities , such as bond length or bond angle .
The Free High School Science Texts (FHSST) organization is a South African non-profit project, which creates open textbooks on scientific subjects. Textbooks are edited to follow the government's syllabus, and published under a Creative Commons license (CC BY [1]), allowing teachers and students to print them or share them digitally.
ICM also is a programming environment for various tasks in computational chemistry and computational structural biology, sequence analysis and rational drug design.The original goal was to develop algorithms for energy optimization of several biopolymers with respect to an arbitrary subset of internal coordinates such as bond lengths, bond angles torsion angles and phase angles.
Coordinate bonds are useful in such supramolecular self-assembly because of their versatile geometries. [1] However, there is controversy over calling coordinate bonds noncovalent, as they are typically strong bonds and have covalent character. [2] The combination of a coordination cage and a guest is a type of inclusion compound. Coordination ...