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Extreme Optimization Mathematics Library for .NET
Curves
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 Mathematics Library for .NET has a simple and
intuitive object model for working with curves. You can easily create the most
common types of curves, find zeroes and calculate derivatives. The Extreme
Optimization Mathematics Library for .NET currently supports
constants, lines, quadratic curves, polynomials and Chebyshev approximations.
In addition, the Extreme Optimization Mathematics Library 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.
In this section:
Curve Basics
Simple Curves
Polynomials
Chebyshev Expansions
Piecewise Curves and Cubic Splines
Comparing Curves and RealFunction Delegates
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