L infty for a function

I have a polynomial p(x) of some degree N>=0 and I need to compute, on some interval [x1,x2], the L_{\infty} norm of the difference sin(x)-p(x).

I try to work in this way, I define sin(x) as v=@(s)sin(s) and p(X) some linear polynomial, e.g. p=@(s)2*s+1. Then how I can continue ?

p.s. I can not take values of the variable x as a vector and take the function norm(...,inf).

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Matt J]

Apply FMINBND to -abs(sin(x)-p(x)).

Or apply FMINSEARCH to the same with an initial guess x0 of the minimizing x.

I can not take values of the variable x as a vector and take the function norm(...,inf).

Even if you ultimately need a continuous-space solution, this is still a good way of generating a reliable initial guess for fminsearch, or similar.

[Matt J]

Do not use syms. fminsearch and fminbnd are numerical solvers. You must pass them function handles rather than symbolic expressions.