  We investigate errors in tangents and adjoints of implicit functions
resulting from errors in the primal solution due to approximations computed by
a numerical solver.
  Adjoints of systems of linear equations turn out to be unconditionally
numerically stable. Tangents of systems of linear equations can become instable
as well as both tangents and adjoints of systems of nonlinear equations, which
extends to optima of convex unconstrained objectives. Sufficient conditions for
numerical stability are derived.
