Function interpolation by solving linear system

For interpolate a data set into an nth degree polynomial, we have to have n + 1 (x,...,(f(x,...))) . It means, for example, that if I want interpolate a data points into a third degree polynomial, I have to be four data points.

Ok, however, if I want, for example, interpolate n + x points (x is a natural number / x > 1) into a nth degree polynomial, I will have a linear system with more equations than variables. Can Matlab solve this interpolation case? For example: can Matlab interpolate sin (x) = z, with x = 0, 0.25, 0.5, 0.75, 1, 1.25,..., 90, into a fifth degree polynomial?

Answer 1

[KSSV]

clc; clear all
x = linspace(0,pi/2,50) ;
y = sin(x) ;
plot(x,y,'r')
n = 5 ;  % order of the polynomial 
p = polyfit(x,y,n) ;

x1 = linspace(0,pi/2,100);
y1 = polyval(p,x1);

hold on
plot(x1,y1,'.b' )

More on: http://in.mathworks.com/help/matlab/ref/polyfit.html

[Lucas]

I spoke sine function just for give an example. What I really wish is to interpolate an arbitrary n + x points (x is natural number and greater than 1) into a nth degree polynomial. For example: I want interpolate 100 points, without know the function it belongs, into a 5th degree function. It's possible in Matlab, without Runge's phenomenon?