guessdegreereturns the minimal degree needed for a polynomial to approximate a function with a certain error on an interval.
guessdegree(f,I,eps,w) : (function, range, constant, function) -> range
f is the function to be approximated.
I is the interval where the function must be approximated.
eps is the maximal acceptable error.
w (optional) is a weight function. Default is 1.
guessdegree tries to find the minimal degree needed to approximate f
on I by a polynomial with an error err=p*w-f whose infinity norm not greater than eps.
More precisely, it finds n minimal such that there exists a
polynomial p of degree n such that ||p*w-f|| < eps.
guessdegree returns an interval: for common cases, this interval is reduced to a
single number (e.g. the minimal degree). But in certain cases, guessdegree does
not succeed in finding the minimal degree. In such cases the returned interval
is of the form [n,p] such that:
no polynomial of degree n-1 gives an error less than eps.
there exists a polynomial of degree p giving an error less than eps.