612 views

Getting an explicit representation of the function returned from Interpolation [duplicate]

I am using Interpolation to get an InterpolatingFunction that fits a set of points. For example, ...
109 views

Determining the analytical equation of an interpolating function [duplicate]

I have the following problem I have the following data ...
117 views

Can Mathematica give the explicit expression of InterpolatingFunction? [duplicate]

As we know, using the function Interpolation[], it will generate an object named InterpolatingFunction, so we can get the derivative, the graphic of the function. But sometimes we need the explicit ...
93 views

Show actual Interpolation function [duplicate]

Is there a command to show the actual function when using the Interpolation command? For example, f = Interpolation[{1, 2, 3, 5, 8, 5}] returns ...
66 views

How does Mathematica interpolates? [duplicate]

In manual for Interpolate function it is said, that possible method of interpolation is Hermite. Unfortunately, I can't see ...
51 views

Is it possible to obtain the algebraic expression of an InterpolatingFunction? [duplicate]

Up until now, I have been trying to obtain an expression for an InterpolatingFunction obtained from NDSolve, by using the ...
3k views

Plotting the Star of Bethlehem

Christmas is around the corner! In preparation, consider the polynomial f[x_,y_]:= 1/10 (4 - x^2 - 2 y^2)^2 + 1/2 (x^2 + y^2) and define $r=(f_x,f_y)$ using the ...
6k views

How to splice together several instances of InterpolatingFunction?

I have a set of InterpolatingFunction returned by NDSolve which are valid over different (but overall continuous) domains. How ...
3k views

Arbitrary precision spline interpolation

The current implementation of Interpolation does not allow arbitrary precision spline interpolation. Yu-Sung Chang says here that "it is not hard to implement it ...
3k views

Interpolating data with a step

Suppose I have some data with a step in it: data = {{1, 1}, {2, 2}, {3, 3}, {3, 4}, {4, 5}, {5, 6}}; Interpolation will complain about this and not give you an ...
3k views

How to calculate the control points of a Bézier curve?

To plot a BezierCurve in Mathematica, I need control points. But, I do not know the control points; I only know the points through which the Bézier curve passes. ...
3k views

Numerically solve an integro-differential equation

So the problem is to numerically solve this Integro-Differential Equation, -v \frac{\:\mathrm{d}\kern0.1mm x(\zeta)}{\:\mathrm{d}\kern0.1mm \zeta} + \psi(\zeta) x(\zeta) + \int_{0}^{\zeta} f(\zeta, \...
2k views

Hermite interpolation

The well known Hermite interpolation uses piecewise cubic polynomials and fits the knot values and derivatives. In contrast the Mathematica piecewise Interpolation ...