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 ...