Computer Science for Numerics

sophisticated. With growing code complexity of numerical libraries grows the need for rigorous Software Engineering methodology:
as provided by Computer Science and state of the art regarding digital processing of discrete data, but lacking in the continuous realm.
We apply, adapt, and extend the classical concepts --- specification, algorithmics, analysis, complexity, verification --- from discrete
bit strings, integers, graphs etc. to real numbers, converging sequences, smooth/integrable functions, bounded operators,
and compact subsets: A new paradigm formalizes mathematical structures as continuous Abstract Data Types with rigorous
Turing-computable semantics but without the hassle of actual Turing machines.