SimplexNumerica provides the following algorithm:
*** Function Plots ***
*** Differentiation ***
*** Integration ***
*** Histograms ***
*** Regression ***
*** Sample Consensus ***
*** Approximation ***
Simplex-Fit
https://en.wikipedia.org/wiki/Simplex_algorithm
The Simplex-Algorithm or shorter Simplex-Fit is a very effective procedure for a nonlinear Fit.
The Simplex algorithm function performs non-linear approximation of all the parameters that
have been in the formula marked to be floated.
As always in non-linear approximation, good starting guesses are essential (for the nonlinear parameters).
Gauß-Fit
The Gauss-Fit proceeds from the same problem definition as the Simplex-Fit.
https://mathematica.stackexchange.com/questions/89246/gauss-fit-to-list-of-2d-points
Bézier-Curves
https://en.wikipedia.org/wiki/B%C3%A9zier_curve
Smoothing Spline
https://en.wikipedia.org/wiki/Smoothing_spline
http://www.rxmlwebtech.org/~tcmlee/PDFfiles/2003csda.pdf
Parametric Smoothing Splines
https://www.sciencedirect.com/science/article/abs/pii/0010448583900854
Cyclic Smoothing Splines
https://www.sciencedirect.com/science/article/abs/pii/0010448583900854
*** Interpolation ***
*** 3D Approximation and Interpolation ***
3D Approximation and Interpolation is sometimes difficult to handle.
The result is very depended from the sample data and the used algorithm.
SimplexNumerica has integrated some different algorithm for 3D fits. The following fits are implemented:
Thin Plate Surface Spline
Thin Plate Surface Spline, or TPS for short, is an interpolation method that finds a "minimally bended"
smooth surface that passes through all given points. TPS of 3 control points is a plane, more than 3
is generally a curved surface and less than 3 is undefined.
Bivariate Cubic Spline
Nearest Neighbor Algorithm
*** Digital Signal Processing ***
*** Envelope Generators ***
*** Discrete Fourier Transform (DFT) ***
*** Fast Fourier Transform (FFT) ***
*** Window Functions ***
*** Goertzel DFT (Filter) ***
*** FIR Filter ***
*** IIR Filter ***
*** Time-series Filter ***
*** Audio Signals ***
*** Array Math Operations ***
*** Math Functions ***
*** Airy Functions ***
*** Elliptic Integrals ***
*** Jacobi Elliptic Functions ***
Riemann Zeta Function (left)
Riemann Zeta Function (right)
*** Outlier Algorithm ***
*** Data Reduction ***
*** Convex Hull ***
*** Inter Lines ***
*** Stochastics ***
*** Peak Detection ***
*** Peak Finder ***
Emission Peak Finder
Absorption Peak Finder
etc.
Simplex Programs IT
Dipl.-Phys.-Ing. Ralf Wirtz
Kasterstr. 30
D-52428 Jülich
Germany
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