Extreme Optimization™: Complexity made simple.

Math and Statistics
Libraries for .NET

  • Home
  • Features
    • Math Library
    • Vector and Matrix Library
    • Statistics Library
    • Performance
    • Usability
  • Documentation
    • Introduction
    • Math Library User's Guide
    • Vector and Matrix Library User's Guide
    • Data Analysis Library User's Guide
    • Statistics Library User's Guide
    • Reference
  • Resources
    • Downloads
    • QuickStart Samples
    • Sample Applications
    • Frequently Asked Questions
    • Technical Support
  • Blog
  • Order
  • Company
    • About us
    • Testimonials
    • Customers
    • Press Releases
    • Careers
    • Partners
    • Contact us
Introduction
Deployment Guide
Nuget packages
Configuration
Using Parallelism
Expand Mathematics Library User's GuideMathematics Library User's Guide
Expand Vector and Matrix Library User's GuideVector and Matrix Library User's Guide
Expand Data Analysis Library User's GuideData Analysis Library User's Guide
Expand Statistics Library User's GuideStatistics Library User's Guide
Expand Data Access Library User's GuideData Access Library User's Guide
Expand ReferenceReference
  • Extreme Optimization
    • Features
    • Solutions
    • Documentation
    • QuickStart Samples
    • Sample Applications
    • Downloads
    • Technical Support
    • Download trial
    • How to buy
    • Blog
    • Company
    • Resources
  • Documentation
    • Introduction
    • Deployment Guide
    • Nuget packages
    • Configuration
    • Using Parallelism
    • Mathematics Library User's Guide
    • Vector and Matrix Library User's Guide
    • Data Analysis Library User's Guide
    • Statistics Library User's Guide
    • Data Access Library User's Guide
    • Reference
  • Mathematics Library User's Guide
    • General Classes
    • Mathematical Functions
    • Complex Numbers
    • Arbitrary Precision Arithmetic
    • Automatic Differentiation
    • Curves and Interpolation
    • Curve Fitting
    • Solving Equations
    • Optimization
    • Calculus
    • Fast Fourier Transforms
    • Random Numbers
    • Generic Arithmetic
    • Appendices
  • Curve Fitting
    • Linear Curve Fitting
    • Nonlinear Curve Fitting
    • Predefined Nonlinear Curves
    • Smoothing
    • Surface fitting and more

Curve Fitting

Extreme Optimization Numerical Libraries for .NET Professional

Curve fitting is the process of finding a curve from a set of curves that best matches a series of data points. The set of curves is defined in terms of curve parameters. In other words, curve fitting consists of finding the curve parameters that produce the best match.

There are different ways to determine what is the 'best' match. If the curve has to go through the data points, we have interpolation. In least squares curve fitting, the sum of the squares of the residuals (the difference between the data value and the value predicted by the curve) is minimized. In weighted least squares, each data point is assigned a weight that indicates how much the data point influences the parameters.

A further distinction is made between linear and nonlinear least squares. In the context of curve fitting, a linear curve is a curve that is linear in its parameters. This is regardless of whether the terms are linear in the curve variable. For example, a quadratic curve, y = ax2+bx+c, is linear in the parameters a, b, and c, even though it is nonlinear in terms of x. On the other hand, the exponential curve y = aebx is linear in a, but nonlinear in b.

The Extreme Optimization Numerical Libraries for .NET contains classes for linear and nonlinear least squares curve fitting.

In this section:

  • Linear Curve Fitting
  • Nonlinear Curve Fitting
  • Predefined Nonlinear Curves
  • Smoothing
  • Surface fitting and more

Copyright (c) 2004-2021 ExoAnalytics Inc.

Send comments on this topic to support@extremeoptimization.com

Copyright © 2004-2021, Extreme Optimization. All rights reserved.
Extreme Optimization, Complexity made simple, M#, and M Sharp are trademarks of ExoAnalytics Inc.
Microsoft, Visual C#, Visual Basic, Visual Studio, Visual Studio.NET, and the Optimized for Visual Studio logo
are registered trademarks of Microsoft Corporation.