  The principle of indirect elimination states that an algorithm for solving
discretized differential equations can be used to identify its own
bad-converging modes. When the number of bad-converging modes of the algorithm
is not too large, the modes thus identified can be used to strongly improve the
convergence. The method presented here is applicable to any standard algorithm
like Conjugate Gradient, relaxation or multigrid. An example from theoretical
physics, the Dirac equation in the presence of almost-zero modes arising from
instantons, is studied. Using the principle, bad-converging modes are removed
efficiently. Applied locally, the principle is one of the main ingredients of
the Iteratively Smooting Unigrid algorithm.
