﻿ Nonlinear Curvefitting: Lorentz Curve Fitting, Sine Curve Fitting, Damped Sinusoid CurveFitting

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# CurvFit (tm): creates algebraic series for fitting ones data. CurvFit (tm) is a nonlinear curve fitting program. Sine, damped Sine, Lorentz, Modified Lorentz, Power (ie Polynomial) and Exponential series are presently available models to match your data. We strongly suggest trying a Lorentz series for data with multiple peaks or valleys. A calculator exists for interpolation &/or extrapolation of given data. CurvFit has proven excellent for hard to fit data. Hard to fit data may take more time -but- it can be done given the right series and parameter values. For start try curve fitting your data with a Lorentz series!

A Lorentz function equals 1 / (1 + a x2). This is a shortened form of the infinite series inverse (1 + Σ ai x2i). For practical purposes the shortened Lorentz function is accurate enough. The Lorentz function equals the derivative of the arctangent.

A Modified Lorentz function equals (1 + x) / (1 + a x2) = (1 + x) * Lorentz function! Use the modified Lorentz when minimizing number of terms in your curve fit series. (Someone suggested that the modified Lorentz is a Bessel function, is it?)

Fitting Sinusoidal data is simplified by finding good initial starting values for given sinusoidal data. In order to do this try our SpectrumSolvers program using a simple spectral estimator (e.g. AutoCorr). A good estimator will calculate key frequencies. Use these key frequency values as initial starting values in CurvFit. Without these good initial frequencies values Curve fitting sinusoidal data can be tough.

Curve fitting is an Inverse Problem in some cases. For example, you might have some Ordinary Differential Equations (ODEs) where you know the solution data points but question some parameters in the ODEs. The target would be your data points and parameter values would be what you are trying to determine. Another example would be determining a electrical circuit parameters when you know the (target) circuit response desired. Curve fit data to model is quick and easy in a Calculus (level) programming language. There are many industry Inverse Problems that exist but are not classified as such.

CurvFit is a increased productivity example do to using Calculus programming ... ie. minutes to solve, days or years to understand solution and what it implies (e.g. wrong model, sampling rate error, etc.). CurvFit helps one learn ...

• Whether math model is good for given data;
• Convergence report tells whether a reasonable solution; and,
• How to select new starting initial parameter values, model, sampling rate error, etc.)

### CurvFit 6.302Source code:

CurvFit was made possible do to a Calculus-level computer language. The source code (fit4user.fc) file is included in order to show the Calculus programming simplicity. CurvFit is a free (4 MB) download.

### CurvFit 6.302Output Plots:

 (Click Any Image To Enlarge) Plot of Error between Data & Curve Both Data & Model Curve on Plot Last Updated: May 29, 2020
First Published: Oct. 13, 1992
OS: Windows XP or newer
Requirements:Windows + Visual Basic 6.0 RunTime files
Publisher: Optimal Designs Enterprise

 Description (Click to download) Price 1. CurvFit: Fits Lorentz, Sine, Damped Sine, etc. series to data. Learn the power of a Lorentz series to fitting real data! 0
 All prices in US Dollars

### Curve Fitting Problems in Industry:

• Abnormal Heart Beats or EKGs;
• Ebola epidemic in West Africa;
• 1918 influenza pandemic in San Francisco, California;
• Many Biological systems; and,
• many many many more!

Free Zoom classes are offered to those interested in one or more of following:

• Curve Fitting Data sets: fitting data to an math expression; Lorentzian, Sine & Damped Sine series are available.
• Calculus-level Coding: learn Calculus-level language in order to solve your math problem.
• Solving Differential Equations: any order, any degree, non-linear, implicit, Boundary and/or Initial Value Problems.

<a href=""><img style="float:left; width:100px" src="https://goal-driven.net/image/curvfit-icon.png"/> <strong>Nonlinear Curvefitting</strong> </a>: Lorentz Curve Fitting, Sine Curve Fitting, Damped Sinusoid CurveFitting, etc. Calculus (level) Problem-Solving for Engineers & Scientists