Interpolation methods

Interpolation techniques. More...

Classes
class	julian::AKIMA
	Class implements the AKIMA interpolation technique. More...
class	julian::CubicInterpolation
	Class implements the cubic local interpolation technique. More...
class	julian::FlatBackward
	Class implements the flat backward interpolation technique. More...
class	julian::FlatForward
	Class implements the flat forward interpolation technique. More...
class	julian::Interpolation
	Class is an abstract type expressing the concept of interpolation. More...
class	julian::LinearInterpolation
	Class implements the linear local interpolation technique. More...
class	julian::LogarithmicInterpolation
	Class implements the logarithmic local interpolation technique. More...
class	julian::NaturalCubicSpline
	Class implements the natural cubic spline interpolation. More...
class	julian::PolynomialInterpolation
	Class implements the polynomial interpolation. More...
class	julian::QuadraticInterpolation
	Class implements the quadratic local interpolation technique. More...
class	julian::SteffenInterpolation
	Class implements the Steffen interpolation. More...

Detailed Description

Interpolation techniques.

An interpolation is a mathematical method of estimating interpolation function (called interpolant) which agrees with values for a given discrete set of points. Usually interpolant has a form of piecewise function - a function that is defined by sub functions, each applying to a certain interval of the function domain. Most common are piecewise linear function or spline functions.

We can distinguish two types of interpolation techniques: local and global. The interpolation methods that are based on "nearest neighbours" points are called local interpolation techniques. They are computational efficient because they do not require fitting to the whole set of points. Major disadvantage of these schemes is that they do not produce interpolant with continuous derivatives. When a continuity of derivatives is a concern, one may use global methods like spline (e.g cubic spline) and sub-spline function (e.g. AKIMA interpolation). The disadvantage of these methods is non-locality, which means that change of value at one node cause changes not only in its surrounding neighbourhood (see [17]), but also at distant intervals.

See more: [1] [4] [45]