# General Chebyshev approximation

I am having trouble understanding it, first of all, what is x? Are x's coefficients of this polynomial we are looking for? This would mean that the polynomial is of degree $$n-1$$ because it has n coefficients? Second of all is this +- notation equal to module? And another question, can anyone give me a simple example of those polynomials and function so I can understand it better? Any help appreciated thanks. :) My example: $$f(t)=|t|$$ , $$t\in[-1,1]$$, if p(x,t) was of degree less or equal to 2 we would be looking for is $$p(x,t))= \frac{1}{2}$$, because of alternans theorem, but in our case it is the polynomial of a degree $$(n-1)$$ so what is an optimal polynomial?...

• The $x$ is a parameter, meaning each $x$ gives a function $p(x,t) = p_x(t)$ in the variable $t$. The $+/-$ means modulus/absolute value. – rubikscube09 Mar 13 at 18:08
• So for instance if $x$ was $(1,0,0,...,0,0,1)$, we would be having a polynomial $p_{x}(t)=t^{n-1}+1$? – ryszard eggink Mar 13 at 18:10