  A re-calibration is proposed for "numerical analysis" as it arises
specifically within the broader, embracing field of modern computer science
(CS). This would facilitate research into theoretical and practicable models of
real-number computation at the foundations of CS, and it would also advance the
instructional objectives of the CS field. Our approach is premised on the key
observation that the great "watershed" in numerical computation is much more
between finite- and infinite-dimensional numerical problems than it is between
discrete and continuous numerical problems. A revitalized discipline for
numerical computation within modern CS can more accurately be defined as
"numerical algorithmic science & engineering (NAS&E), or more compactly, as
"numerical algorithmics," its focus being the algorithmic solution of numerical
problems that are either discrete, or continuous over a space of finite
dimension, or a combination of the two. It is the counterpart within modern CS
of the numerical analysis discipline, whose primary focus is the algorithmic
solution of continuous, infinite-dimensional numerical problems and their
finite-dimensional approximates, and whose specialists today have largely been
repatriated to departments of mathematics. Our detailed overview of NAS&E from
the viewpoints of rationale, foundations, and organization is preceded by a
recounting of the role played by numerical analysts in the evolution of
academic departments of computer science, in order to provide background for
NAS&E and place the newly-emerging discipline within its larger historical
context.
