Least squaresThe method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.
Control theoryControl theory is a field of control engineering and applied mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a desired state, while minimizing any delay, overshoot, or steady-state error and ensuring a level of control stability; often with the aim to achieve a degree of optimality. To do this, a controller with the requisite corrective behavior is required.
Monte Carlo methodMonte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to use other approaches. Monte Carlo methods are mainly used in three problem classes: optimization, numerical integration, and generating draws from a probability distribution.
Carbonyl groupIn organic chemistry, a carbonyl group is a functional group with the formula , composed of a carbon atom double-bonded to an oxygen atom, and it is divalent at the C atom. It is common to several classes of organic compounds (such as aldehydes, ketones and carboxylic acids), as part of many larger functional groups. A compound containing a carbonyl group is often referred to as a carbonyl compound. The term carbonyl can also refer to carbon monoxide as a ligand in an inorganic or organometallic complex (a metal carbonyl, e.
