30 Apr 2009
24 Jun 2014)
Numerical computation with functions instead of numbers.
function pass = remeztest
% The REMEZ command constructs infinity-norm
% best approxoimations. This test confirms
% that the answers come out right for two simple
% cases of polynomial approximations.
% The second text compares the result of REMEZ with
% that of CF, so it is also a test of CF.
% (A Level 1 test)
% Nick Trefethen, 27 March 2009
% Test remez:
x = chebfun('x',[-1 1]);
f = abs(x) + x;
pexact = .5+x;
pbest = remez(f,1);
err = norm(pbest-pexact);
pass(1) = (err<1e-10);
% Test remez and cf:
f = exp(sin(exp(x)));
pcf = cf(f,7);
pbest = remez(f,7);
pass(2) = (norm(pcf-pbest)<0.0003);