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In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations.
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one [clarification needed] effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values ...
Let (,) be a real dynamical system with degrees of freedom. Here is the configuration space and = (, (), ()) the Lagrangian, i.e. a smooth real-valued function such that (), and () is an -dimensional "vector of speed".
In the more general multiple regression model, there are independent variables: = + + + +, where is the -th observation on the -th independent variable.If the first independent variable takes the value 1 for all , =, then is called the regression intercept.
The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern.
The quadratic formula can equivalently be written using various alternative expressions, for instance = (), which can be derived by first dividing a quadratic equation by , resulting in + + = , then substituting the new coefficients into the standard quadratic formula.
In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter (the combined center of mass) or, if one body is much more massive than the other bodies of the system combined, its speed relative to the center of mass of the most massive body.
Pakistan, [e] officially the Islamic Republic of Pakistan, [f] is a country in South Asia.It is the fifth-most populous country, with a population of over 241.5 million, [c] having the second-largest Muslim population as of 2023.