  While concepts and tools from Theoretical Computer Science are regularly
applied to, and significantly support, software development for discrete
problems, Numerical Engineering largely employs recipes and methods whose
correctness and efficiency is demonstrated empirically.
  We advertise REAL COMPLEXITY THEORY: a resource-oriented foundation to
rigorous computations over continuous universes such as real numbers, vectors,
sequences, continuous functions, and Euclidean subsets: in the bit-model by
approximation up to given absolute error. It offers sound semantics (e.g. of
comparisons/tests), closure under composition, realistic runtime predictions,
and proofs of algorithmic optimality by relating to known classes like NP, #P,
PSPACE.
