  Numerical software are widely used in safety-critical systems such as
aircrafts, satellites, car engines and so on, facilitating dynamics control of
such systems in real time, it is therefore absolutely necessary to verify their
correctness. It is a long standing challenge to guarantee verified properties
of numerical software are indeed satisfied by their real behaviours, because
most of these verifications are conducted under ideal mathematical models, but
their real executions could be influenced essentially by uncertain inputs
accounting for round-off errors and additive perturbations from real-world
phenomena to hardware, which are abstracted away in these ideal mathematical
models. In this paper, we attempt to address this issue focusing on
nontermination analysis of numerical software, where nontermination is often an
unexpected behaviour of computer programs and may be problematic for
applications such as real-time systems having hard deadlines on transaction
execution time, and propose a method for robust conditional nontermination
analysis, which can be used to under-approximate the maximal robust
nontermination input set for a given program, from which the program never
terminates, regardless of the aforementioned disturbances. Finally, several
examples are employed to illustrate our approach.
