This work grew out of several years of research, graduate seminars
and talks on the subject. It was motivated by a desire to make the
technology accessible to those who most needed it or could most use
it. It is meant to be a self-contained introduction, a reference
for the techniques, and a guide to the literature for the
underlying theory. It contains pointers to fertile areas for future
research. It also serves as introductory documentation for a
Fortran 90 software package for nonlinear systems and global
optimization. The subject of the monograph is deterministic,
automatically verified or r- orous methods. In such methods,
directed rounding and computational fix- point theory are combined
with exhaustive search (branch and bound) te- niques. Completion of
such an algorithm with a list of solutions constitutes a rigorous
mathematical proof that all of the solutions within the original
search region are within the output list. The monograph is
appropriate as an introduction to research and technology in the
area, as a desk reference, or as a graduate-level course reference.
Kno- edge of calculus, linear algebra, and elementary numerical
analysis is assumed.
General
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