[Feature Request] Interpolating Polynomials

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Description

Interpolating polynomials are polynomials of degree=n-1. This degree is sufficient flexible to interpolate all present data points.
The construction of the linear system of equations is straight forward and does not require expensive construction of least-squares linear systems. Additionally the least-squares approach present in Fitting.LinearRegression.Polynomial does not inevitably converge to a interpolating polynomial.

Repro steps

try to interpolate the following data with polynomial regression
let x_DataH = vector [0.;10.;30.;50.;70.;80.;82.]
let y_DataH = vector [150.;200.;200.;200.;180.;100.;0.]

Expected behavior

An interpolating curve.

Actual behavior

The first knot at x=0 is missed by the curve.

Solution

Construct a linear system of equations that has a unique solution and interpolates all given knots.

Related information

Presentation_Seminar

Lecture

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closed by b8e72d3