This issue contains full, traditionally refereed papers with topics presented at the
Validated Computing 2002 conference, held in Toronto, May 23 to May 25, 2002.
See  for a review of that conference and see the web page:
for the conference program. The papers in this issue represent the ﬁrst of the
twenty submitted full-length works to be accepted; we anticipate an additional
issue containing more of these works.
Keeping with the overall conference theme of honoring the contributions of
Ramon Moore over the past half-century, Louis Rall, in “Evaluation of Functions,
Gradients, and Jacobians,” provides a lucid and concise overview of automatic
differentiation, including use of the structure of the process in validation of the
results. (Rall asserts that Ramon Moore, in addition to originating interval analysis
in its present form, originated automatic differentiation.)
Robust geometric computations are one of the application areas that have ben-
eﬁtted most from interval computations. Along these lines, Jo
ao Batista Oliviera
and Luiz Henrique de Figueiredo present an algorithm for “Robust Approximation
of Offsets, Bisectors, and Medial Axes of Plane Curves.” The careful explana-
tions, inclusion of background material, and insightful illustrations make this work
In “Numerical Experiences with a New Generalized Subinterval Selection Crite-
rion for Interval Global Optimization,” Tibor Csendes studies a heuristic to increase
the efﬁciency of interval branch and bound algorithms for global optimization.
In contrast to his previous works on the subject, Csendes studies the effect of
this heuristic in practical algorithms involving interval Newton methods and other
acceleration devices, in addition to the heuristic’s effect within the simple “Moore–
Skelboe” algorithm. The numerical experiments are carefully reported.
With “Estimating and Validating the Cumulative Distribution of a Function of
Random Variables: Toward the Development of Distribution Arithmetic,” Weldon
Lodwick and K. David Jamison contribute to the burgeoning ﬁeld of applications
of intervals and interval uncertainty to statistics. Also in the general area of statis-
tical analysis veriﬁed with interval computations, Daniel Berleant, Lizhi Xie and