In this answer I found a very useful approach to easily center certain elements in a alignat environment using a new command:
\newcommand{\ccol}[1]{\omit\hfill $#1$\hfill}
I inserted the $’s because \omit seems to terminate math mode.
\begin{alignat}{3}
x_{n}-\frac{f\left(x_{n}\right)}{f^{\prime}\left(x_{n}\right)}-x^{\ast}=\mbox{} & x_{n+1}-x^{\ast} & \mbox{}=\mbox{} & \left(x_{n}-x^{\ast}\right)^{2} & \mbox{}\cdot\frac{f^{\prime\prime}\left(\xi\right)}{2\cdot f^{\prime}\left(x_{n}\right)}\\
& \ccol{\epsilon_{n+1}} & \mbox{}=\mbox{} & \ccol{\epsilon_{n}^{2}} & \mbox{}\cdot\frac{f^{\prime\prime}\left(\xi\right)}{2\cdot f^{\prime}\left(x_{n}\right)}
\end{alignat}
Unfortunately, the numbering of the second equation is gone. Even using another command to manually activate numbering for certain equations in alignat* results in the above:
\newcommand\numberthis{\addtocounter{equation}{1}\tag{\theequation}}
\begin{alignat*}{3}
x_{n}-\frac{f\left(x_{n}\right)}{f^{\prime}\left(x_{n}\right)}-x^{\ast}=\mbox{} & x_{n+1}-x^{\ast} & \mbox{}=\mbox{} & \left(x_{n}-x^{\ast}\right)^{2} & \mbox{}\cdot\frac{f^{\prime\prime}\left(\xi\right)}{2\cdot f^{\prime}\left(x_{n}\right)}\numberthis\\
& \ccol{\epsilon_{n+1}} & \mbox{}=\mbox{} & \ccol{\epsilon_{n}^{2}} & \mbox{}\cdot\frac{f^{\prime\prime}\left(\xi\right)}{2\cdot f^{\prime}\left(x_{n}\right)}\numberthis
\end{alignat*}
How to not omit numbering?



\leftand\right. Developers of LyX should read this site and the uncountable times we say “don't abuse\leftand\right”. – egreg Sep 14 '15 at 21:21\left? If you put in(, I don't believe LyX will change it. If you add "smart" parentheses (e.g. through delimiters dialog) then yes theleftis added. – scottkosty Sep 15 '15 at 02:33