Reliable Computations and Their Applications
ATechnical Track at the 20th ACM Symposium on Applied Computing
Santa Fe, New Mexico, USA, March 13–17, 2005
For the past twenty years, the ACM Symposium on Applied Computing has been
a primary gathering forum for applied computer scientists, computer engineers,
software engineers, and application developers from around the world.
2. RCA Track: Motivations
Many numerical computations, be they solutions to systems of differential equa-
tions or optimization problems coming from applied areas like protein folding, do
not provide us with guaranteed computation results. In many situations, we have
numerical solutions, we may even have a theorem guaranteeing that eventually,
this numerical solution tends to the actual precise one, but the algorithm itself does
not provide us with guaranteed bounds on the difference between the numerical
approximate solution and the desired actual one.
Therefore, in some practical situations, numerical solutions are much farther
from the actual (unknown) precise solutions than the users assume. As a result, we
often end up with inefﬁcient local maxima for practical optimization problems like
chemical engineering—or even with a mission failure if we are planning, e.g., a
For some such algorithms, researchers have found guaranteed bounds, but pro-
ducing a guaranteed bound for each algorithm requires a lot of work.
It is therefore desirable to develop a methodology that would provide algorithms
with automatic result veriﬁcation, i.e., with automatically generated upper bound
on the difference between the actual and the numerical solution. In other words, we
need computation techniques that produce reliable (guaranteed) results.