  An apriori bound for the condition number associated to each of the following
problems is given: general linear equation solving, minimum squares,
non-symmetric eigenvalue problems, solving univariate polynomials, solving
systems of multivariate polynomials. It is assumed that the input has integer
coefficients and is not on the degenerate locus of the respective problem (i.e.
the condition number is finite). Then condition numbers are bounded in terms of
the dimension and of the bit-size of the input.
  In the same setting, bounds are given for the speed of convergence of the
following iterative algorithms: QR without shift for the symmetric eigenvalue
problem, and Graeffe iteration for univariate polynomials.
