Let $A(x)\in \mathbb{R}^{n\times n}$ be a matrix depending on $x$, $b\in \mathbb{R}^n$ such that, $$A(x)x=b,$$ i.e. we have a system of non linear equations. Let $u\in \mathbb{R}^n$ be its solution and $u_h\in \mathbb{R}^n$ be its approximate solution. Define $R(x)$ as the residue of the above system, i.e., $R(x)=A(x)x-b$.
Say $\|R(x)\|_{l^2}\leq \varepsilon$ where $\varepsilon$ is some tolerance (say clsoe to $10^{-7}$) and $\|.\|_{l^2}$ is the $l^2$ norm.. Then can we say $\|u-u_h\|_{\infty}\leq 1$? Do we have any closeness between approximate and analytical solution?