Aim of the applet

Interpolation of a table of points or of a function by means of polynomials of minor degree or like three.

Try first with a table of points that represents a function.

Insert points with the tool and calculate the resul spline.

Represent a function in the graph, take points on it and calculate the approximation with splines.

Input data

Via keyboard:


• Table with the points and its images. Points can be added with extra cells press on "Add".
• Derivative comes second of the ends of the spline.
• If you want, a function of variable x.

Output data

Graphical representation of the cubic spline that goes through the given points.

Table of results where we have the expression of the cubic spline in every interval.

First steps

To use the function f (x) = x³ + x in the interval [-1,2].

We know that:

f'= 3x²+1

f'' = 6x

Then the value of S''₀ y S''_n es:

S''₀ = S''(-1) = -6.

S''_n = S''(2) = 12.

To verify that the expression of the spline is: -2 + (x + 1)(4 + (x + 1)(-3 + x + 1)) that simplified return the first function f(x) = x³ + x.

To try like, if there changes the value of the second derivatives S''₀ y S''_n, changes both the expression of the spline and his graph.

Observations

If you use the table to define points, make sure they are ordered.