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Domain coloring plot of the function f(x) = (x 2 − 1)(x − 2 − i) 2 / x 2 + 2 + 2i , using the structured color function described below. In complex analysis, domain coloring or a color wheel graph is a technique for visualizing complex functions by assigning a color to each point of the complex plane. By assigning points on the ...
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.
The following MATLAB code will plot the root locus of the closed-loop transfer function as varies using the described manual method as well as the rlocus built-in function: % Manual method K_array = ( 0 : 0.1 : 220 ). ' ; % .' is a transpose.
The maximum correlation coefficient corresponds to the optimal value of the shape parameter. For better precision, two iterations of the PPCC plot can be generated; the first is for finding the right neighborhood and the second is for fine tuning the estimate. The PPCC plot is used first to find a good value of the shape parameter.
Plot of the Whittaker function M k,m(z) with k=2 and m= 1 / 2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D In mathematics, a Whittaker function is a special solution of Whittaker's equation, a modified form of the confluent hypergeometric equation introduced by Whittaker () to make the formulas involving the solutions more ...
A Nichols plot. The Nichols plot is a plot used in signal processing and control design, named after American engineer Nathaniel B. Nichols. [1] [2] [3] It plots the phase response versus the response magnitude of a transfer function for any given frequency, and as such is useful in characterizing a system's frequency response.
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 ...
A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system (here n = 2).