Beispiel - SAM - ETH Zürich

Listing 2.1: Berechung approximativer Maximumnorm des Fehlers bei Polynominterpolation
1 f u n c t i o n errinf = polyintperr(fun,nodes,span)
2 % Error of polynomial interpolation in maximum norm
3 % fun : handle to function to be interpolated
4 % nodes : interpolation nodes
5 % span : evaluation interval (default [-1,1])
6
7 i f (nargin < 3), span = [-1,1]; end
8 n = length(nodes);
9
0 fval = zeros(1,n);
1 f o r j=1:n, fval(j) = fun(nodes(j)); end
2
3 p = p o l y f i t(nodes,fval,n-1); % built-in polynomial interpolation
4
5 % Compute maximum norm by sampling on fine mesh
6 N = 1000*n;
7 t = span(1) + (0:N)*(span(2)-span(1))/N;
8 pval = polyval(p,t);
9 fval = zeros(1,N+1);
0 f o r j=1:N+1, fval(j) = fun(t(j)); end
1 errinf = max(abs(pval-fval));
Listing 2.2: Berechung approximativer Maximumnorm des Interpolationsfehlers in Gausspunkten
Numerische
Mathemtik
R. Hiptmair
rev 35327,
25. April
2011
2.2
p. 189