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Software FindGraph Rationals.

A simple empirical model

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Select empirical model, specify equation form, and perform your fit
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The curve fitting often starts with choosing a model form. But sometimes your goal is simple. For example, you want to get a smooth curve to make a graph look attractive. Polynomial models are often used for this purpose. The main disadvantage of polynomial models is that they may be unstable.

Specify model: rationals FindGraph suggests rational models, Fourier approximation, Neural Networks, B-splines and parametric curves. Rational models are often used when a simple empirical model is required. The main advantage of rationals is their flexibility with data that has complicated structure.
To find fit in form of rationals, start the Wizard of Approximation and specify model: rationals.

Perform your fit and find equation Model is defined as ratios of polynomials. The degree N of nominator and the degree M of denominator vary in limits upto 12. Perform your fit and find equation.

A simple empirical model might provide a reasonably accurate values considering their uncomplicated approach and data availability. The graphical fit results shown below indicate that the fits and residuals for the rational equation are good enough. The user can even include error bars and confidence bands to the graph.
A simple empirical model
If you don't have to interpret and analyze the best fit values, use nonlinear regression to find a model empirically.

Read more about:

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Curve fitting Curve fitting
Best-fit Best-fit equation
Closed curves Closed curves
Library Library
Analysis Analysis
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Convolution Convolution
Extract of periodic signals Periodic signals
Procrustes analysis Procrustes analysis
SSA forecasting SSA forecasting

 

 

 

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