Abstract:
The paper gives a brief review of tolerance space theory and develops its applications to
finding almost solutions (i.e., functions that, substituted into the given equation,
satisfy it up to a small numerical error) for equations of different types, providing
existence theorems (proved by homological methods) of almost solutions for a wide variety
of equations.
Keywords:tolerance space, almost solution, almost fixed point, difference scheme, homology,
homotopy, Lefshetz number.
