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MATLAB (an abbreviation of "MATrix LABoratory" [22]) is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks.MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages.
Linear least squares (LLS) is the least squares approximation of linear functions to data. It is a set of formulations for solving statistical problems involved in linear regression , including variants for ordinary (unweighted), weighted , and generalized (correlated) residuals .
Since the graph of an affine(*) function is a line, the graph of a piecewise linear function consists of line segments and rays. The x values (in the above example −3, 0, and 3) where the slope changes are typically called breakpoints, changepoints, threshold values or knots.
In optimization, line search is a basic iterative approach to find a local minimum of an objective function:. It first finds a descent direction along which the objective function f {\displaystyle f} will be reduced, and then computes a step size that determines how far x {\displaystyle \mathbf {x} } should move along that direction.
Linear quantile regression models a particular conditional quantile, for example the conditional median, as a linear function β T x of the predictors. Mixed models are widely used to analyze linear regression relationships involving dependent data when the dependencies have a known structure. Common applications of mixed models include ...
The pseudo-Voigt profile (or pseudo-Voigt function) is an approximation of the Voigt profile V(x) using a linear combination of a Gaussian curve G(x) and a Lorentzian curve L(x) instead of their convolution. The pseudo-Voigt function is often used for calculations of experimental spectral line shapes.
A constant function is also considered linear in this context, as it is a polynomial of degree zero or is the zero polynomial. Its graph, when there is only one variable, is a horizontal line. In this context, a function that is also a linear map (the other meaning) may be referred to as a homogeneous linear function or a linear form.
Nelder–Mead (Downhill Simplex) explanation and visualization with the Rosenbrock banana function; John Burkardt: Nelder–Mead code in Matlab - note that a variation of the Nelder–Mead method is also implemented by the Matlab function fminsearch. Nelder-Mead optimization in Python in the SciPy library.