How can I avoid a 'Dimension too large' error in an a0 size TikZ figure?

Update

The problem appears only with the edges. A possibility is to scale only the edges. Firstly we get the coordinates, then we divide them by 10 and finally we scale the coordinates by 10. I changed some styles from the original code.

\documentclass[onlymath]{beamer}
\usefonttheme{serif}
\usepackage[orientation=portrait,size=a0,scale=1.0]{beamerposter}
\usepackage{eulervm}
\usepackage{tikz}
\usetikzlibrary{shapes,arrows,positioning,matrix}

\begin{document}
\begin{frame}[t,fragile]{}

  \begin{block}{Big TikZ Test}
  \begin{center}

    \begin{tikzpicture}[blk/.style= {rectangle,draw,text width=2in,text centered},
                       edge/.style = {draw =black!50 ,line width=3pt,->}]

      \matrix[row sep=1cm,column sep=1cm] {%
        \node[blk] (a) {A};
        &
        \node[blk] (b) {B};
        &
        \node[blk] (c) {C};
        &
        \node[blk] (d) {D};
        &
        \node[blk] (e) {E};
        &
        \node[blk] (f) {F};
        &
        \node[blk] (g) {G};
        &
        \node[blk] (h) {H};
        &
        \node[blk] (i) {I};
        &
        \node[blk] (j) {J};
        \\
      };

      \path[edge] (j) edge [bend left=30] (i)
                      edge [bend left=30] (h)
                      edge [bend left=30] (g)
                      edge [bend left=30] (f)
                      edge [bend left=30] (e);

\path (a.south);
\pgfgetlastxy{\ax}{\ay} 
\path (b.south);
\pgfgetlastxy{\bx}{\by}   
\path (c.south);
\pgfgetlastxy{\cx}{\cy}   
\path (d.south);
\pgfgetlastxy{\dx}{\dy}   
       \begin{scope} [scale=10]
        \path[edge] (j) edge [bend left=30] (0.1*\dx,0.1*\dy)
                        edge [bend left=30] (0.1*\cx,0.1*\cy)
                        edge [bend left=30] (0.1*\bx,0.1*\by)
                        edge [bend left=30] (0.1*\ax,0.1*\ay);    
       \end{scope}     
    \end{tikzpicture}
  \end{center}
  \end{block}
\end{frame}
\end{document} 

There is another problem, when we crate the edges, in the log I see

Missing character: There is no ï in font nullfont!
Missing character: There is no ¿ in font nullfont!
Missing character: There is no ¼ in font nullfont!
Missing character: There is no ï in font nullfont!
Missing character: There is no ¿ in font nullfont!
Missing character: There is no ¼ in font nullfont!
Missing character: There is no ï in font nullfont!
Missing character: There is no ¿ in font nullfont!
Missing character: There is no ¼ in font nullfont! 

One warning for one edge

update 2

Perhaps it's a bug in 'to'. I try with controls and the code compiles without errors. I used some control points but without calculations.

\begin{tikzpicture}[blk/.style= {rectangle,draw,text width=2in,text centered},
                   edge/.style = {draw =black!50 ,line width=3pt,->}]

  \matrix[row sep=1cm,column sep=1cm] {%
    \node[blk] (a) {A};
    &
    \node[blk] (b) {B};
    &
    \node[blk] (c) {C};
    &
    \node[blk] (d) {D};
    &
    \node[blk] (e) {E};
    &
    \node[blk] (f) {F};
    &
    \node[blk] (g) {G};
    &
    \node[blk] (h) {H};
    &
    \node[blk] (i) {I};
    &
    \node[blk] (j) {J};
    \\
  };

  \path[edge] (j) edge [bend left=30] (i)
                  edge [bend left=30] (h)
                  edge [bend left=30] (g)
                  edge [bend left=30] (f)
                  edge [bend left=30] (e);
  \path[edge] (j) .. controls ([{shift=(210:20)}]j) and ([{shift=(-30:20)}]d) .. (d);
  \path[edge] (j) .. controls ([{shift=(210:25)}]j) and ([{shift=(-30:25)}]c) .. (c);
  \path[edge] (j) .. controls ([{shift=(210:30)}]j) and ([{shift=(-30:30)}]b) .. (b);
  \path[edge] (j) .. controls ([{shift=(210:35)}]j) and ([{shift=(-30:35)}]a) .. (a);    

\end{tikzpicture}  

use

\begin{tikzpicture}[scale=10]
  \tikzstyle{blk} = [rectangle,draw,text width=0.2in,text centered];
  \tikzstyle{edge} = [draw,line width=0.5pt,black!50];
  \matrix[row sep=0.1cm,column sep=0.1cm] {