Everybody is current in a world surrounded by computer. Computers
determine our professional activity and penetrate increasingly deeper
into our everyday life. Therein we also need increasingly refined c-
puter technology. Sometimes we think that the next generation of c-
puter will satisfy all our dreams, giving us hope that most of our
urgent problems will be solved very soon. However, the future comes and
il- sions dissipate. This phenomenon occurs and vanishes sporadically,
and, possibly, is a fundamental law of our life. Experience shows that
indeed 'systematically remaining' problems are mainly of a complex tech-
logical nature (the creation of new generation of especially perfect -
croschemes, elements of memory, etc. ). But let us note that amongst
these problems there are always ones solved by our purely intellectual
efforts alone. Progress in this direction does not require the invention
of any 'superchip' or other similar elements. It is important to note
that the results obtained in this way very often turn out to be more
significant than the 'fruits' of relevant technological progress. The
hierarchical asymptotic analytical-numerical methods can be - garded as
results of such 'purely intellectual efforts'. Their application allows
us to simplify essentially computer calculational procedures and,
consequently, to reduce the calculational time required. It is obvious
that this circumstance is very attractive to any computer user.