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30 Apr 2009 (Updated )

Numerical computation with functions instead of numbers.

Editor's Notes:

This file was selected as MATLAB Central Pick of the Week

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);

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