"+1">Purpose</FONT></B>
<PRE>
  To balance a pair of N-by-N real matrices (A,B). This involves,
  first, permuting A and B by equivalence transformations to isolate
  eigenvalues in the first 1 to ILO-1 and last IHI+1 to N elements
  on the diagonal of A and B; and second, applying a diagonal
  equivalence transformation to rows and columns ILO to IHI to make
  the rows and columns as close in 1-norm as possible. Both steps
  are optional. Balancing may reduce the 1-norms of the matrices,
  and improve the 