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    • General Classes
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  • Curves and Interpolation
    • Curve Basics
    • Polynomials
    • Chebyshev Series
    • Barycentric Series
    • Piecewise Curves and Cubic Splines
    • Cubic Splines
    • Comparing Curve classes and delegates

Curves and Interpolation

Extreme Optimization Numerical Libraries for .NET Professional

For our purposes, a curve is a possibly curved line showing a relationship between two factors. Corresponding to every value of the variable x we have a value y = f(x ). In programming terms, this is similar to a method that takes one Double argument and returns a Double.

Curves are also known as functions. However, because the word function is a reserved word in many languages, including Visual Basic .NET, we chose the term Curve to represent functions. In the documentation, both curve and function may be used.

The Extreme Optimization Numerical Libraries for .NET has a simple and intuitive object model for working with curves. You can easily create the most common types of curves, find zeros and calculate derivatives. The Extreme Optimization Numerical Libraries for .NET currently supports polynomials, Chebyshev series, piecewise curves including several types of cubic splines, and a wide variety of nonlinear curves.

In addition, the Extreme Optimization Numerical Libraries for .NET implements the notion of a function basis. A function basis is a set of functions that can be combined to form a particular class of functions or curves. An example of a function basis is the set of monomial functions 1, x, x2, x3, which can be combined to form all polynomials up to degree 3. Function bases have applications in least squares problems and interpolation.

  • Curve Basics
  • Polynomials
  • Chebyshev Series
  • Piecewise Curves and Cubic Splines
  • Cubic Splines
  • Comparing Curve classes and delegates

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