Name:

supnorm computes an interval bounding the supremum norm of an approximation error (absolute or relative) between a given polynomial and a function.

Usage:

supnorm(p, f, I, errorType, accuracy) : (function, function, range, absolute|relative, constant) -> range

Parameters:

Description:

Example 1:

   > p = remez(exp(x), 5, [-1;1]);
   > midpointmode=on!;
   > supnorm(p, exp(x), [-1;1], absolute, 2^(-40));
   0.452055210438~2/7~e-4

Example 2:

   > prec=200!;
   > midpointmode=on!;
   > d = [1;2];
   > f = exp(cos(x)^2 + 1);
   > p = remez(1,15,d,1/f,1e-40);
   > theta=1b-60;
   > prec=default!;
   > mode=relative;
   > supnorm(p,f,d,mode,theta);
   0.30893006200251428~5/6~e-13

Example 3:

   > midpointmode=on!;
   > mode=relative;
   > theta=1b-135;
   > d = [-1b-2;1b-2];
   > f = expm1(x);
   > p = x * (1 +  x * ( 2097145 * 2^(-22) + x * ( 349527 * 2^(-21) + x * (87609 * 2^(-21) + x * 4369 * 2^(-19)))));
   > theta=1b-40;
   > supnorm(p,f,d,mode,theta);
   0.98349131972~2/3~e-7
See also: dirtyinfnorm, infnorm, checkinfnorm, absolute, relative, taylorform, autodiff, numberroots, diam
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