Column width adjustment in tabularx environment

Question

I was trying to adjust my table column width from a similar post here multicolumn tabularx extending page width. But this got me into another problem where the alignment of the header for the last three column is not centred over the last three columns.

I have been trying to figure this out myself for quite a while without much success. Any help would be highly appreciated.

Here is my code for the table using the package tabularx.

\begin{table}[ht]
\renewcommand\arraystretch{1.5}
\newcolumntype{c}{>{\centering\arraybackslash\hspace{0pt}}X}
\centering
\begin{tabularx}{\textwidth}{@{} l *{2}{c} *{3}{c} @{}}
\toprule
$n$ & 
\multicolumn{1}{c}{Old iteration scheme} & 
\multicolumn{1}{c}{New iteration scheme} & 
\multicolumn{3}{c}{Rate of Convergence} \\ 
\cmidrule(lr){4-6} % left- and right-trimming
& $u_n$ & $x_n$ & $|u_n-1|$ & $|x_n-1|$ & $\frac{|x_n-1|}{|u_n-1|}$ \\ 
\midrule
1 & 1.15489 & 1.04139 & 0.154895 & 0.0413883 & 0.267203\\ 
2 & 1.02536 & 1.00041 & 0.025363 & 0.000411711 & 0.0162327\\
3 & 1.00201 & 1.00000 & 0.00201099 & 4.34451$\times10^{-8}$ & 0.0000216038\\
4 & 1.00012 & 1.00000 & 0.000123976 & 4.44089$\times10^{-16}$ & 3.58206$\times10^{-12}$\\
5 & 1.00001 & 1.00000 & 7.46682$\times10^{-6}$ & 0.00000 & 0.000000\\
6 & 1.00000 & 1.00000 & 4.49177$\times10^{-7}$ & 0.00000 & 0.000000\\
7 & 1.00000 & 1.00000 & 2.70198$\times10^{-8}$ & 0.00000 & 0.000000\\
\bottomrule
\end{tabularx}
\caption{Rate of Convergence}
\end{table}

Answer 1

Using a newly defined C (upper case) column type instead of redefining the c (lower case) type, results in the following output: (Side note: the table could be too wide for the textwidth. Depending on your documentclass, font and margin sizes, you might have to adjust the code to account for that). In the following MWE, I also included an example based on tabular* instead of tabularx:

\documentclass{article}
\usepackage{geometry}
\usepackage{tabularx}
\usepackage{booktabs}
\usepackage{makecell}
\renewcommand{\theadfont}{\normalsize}

\begin{document}

\begin{table}[ht]
\renewcommand\arraystretch{1.5}
\newcolumntype{C}{>{\centering\arraybackslash\hspace{0pt}}X}
\centering
\begin{tabularx}{\textwidth}{@{} l *{5}{C} @{}}
\toprule
$n$ & 
\multicolumn{1}{C}{Old iteration scheme} & 
\multicolumn{1}{C}{New iteration scheme} & 
\multicolumn{3}{c}{Rate of Convergence} \\ 
\cmidrule(lr){4-6} % left- and right-trimming
& $u_n$ & $x_n$ & $|u_n-1|$ & $|x_n-1|$ & $\frac{|x_n-1|}{|u_n-1|}$ \\ 
\midrule
1 & 1.15489 & 1.04139 & 0.154895 & 0.0413883 & 0.267203\\ 
2 & 1.02536 & 1.00041 & 0.025363 & 0.000411711 & 0.0162327\\
3 & 1.00201 & 1.00000 & 0.00201099 & 4.34451$\times10^{-8}$ & 0.0000216038\\
4 & 1.00012 & 1.00000 & 0.000123976 & 4.44089$\times10^{-16}$ & 3.58206$\times10^{-12}$\\
5 & 1.00001 & 1.00000 & 7.46682$\times10^{-6}$ & 0.00000 & 0.000000\\
6 & 1.00000 & 1.00000 & 4.49177$\times10^{-7}$ & 0.00000 & 0.000000\\
7 & 1.00000 & 1.00000 & 2.70198$\times10^{-8}$ & 0.00000 & 0.000000\\
\bottomrule
\end{tabularx}
\caption{Rate of Convergence}
\end{table}


\begin{table}[ht]
\centering
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} l *{5}{c} @{}}
\toprule
$n$ & 
\multicolumn{2}{c}{iteration scheme} & 
\multicolumn{3}{c}{Rate of Convergence} \\
\cmidrule(r){2-3} \cmidrule(l){4-6}
& old & new \\ 
& $u_n$ & $x_n$ & $|u_n-1|$ & $|x_n-1|$ & $\frac{|x_n-1|}{|u_n-1|}$ \\ 
\midrule
1 & 1.15489 & 1.04139 & 0.154895 & 0.0413883 & 0.267203\\ 
2 & 1.02536 & 1.00041 & 0.025363 & 0.000411711 & 0.0162327\\
3 & 1.00201 & 1.00000 & 0.00201099 & 4.34451$\times10^{-8}$ & 0.0000216038\\
4 & 1.00012 & 1.00000 & 0.000123976 & 4.44089$\times10^{-16}$ & 3.58206$\times10^{-12}$\\
5 & 1.00001 & 1.00000 & 7.46682$\times10^{-6}$ & 0.00000 & 0.000000\\
6 & 1.00000 & 1.00000 & 4.49177$\times10^{-7}$ & 0.00000 & 0.000000\\
7 & 1.00000 & 1.00000 & 2.70198$\times10^{-8}$ & 0.00000 & 0.000000\\
\bottomrule
\end{tabular*}
\caption{Rate of Convergence}
\end{table}
\end{document}