#
On the Set of Euclidean Distance Matrix Completions

##
Henry Wolkowicz, University of Waterloo

### work with Abdo Alfakih, University of Windsor

**ABSTRACT**

A partial pre-distance matrix **W=(w**_{ij})
is a matrix
with zero diagonal and with certain elements *fixed*
to given nonnegative
values; the other elements are considered *free*.
The **EDM completion problem** chooses nonnegative values for the
free elements in order to obtain a Euclidean distance matrix,
**EDM**. The nearest (or approximate)
EDM problem is to find a Euclidean distance matrix
that is nearest
in the Frobenius norm to the matrix **A**, when the free variables are
discounted.
Applications for EDM include: molecular conformation problems in
chemistry;
multidimensional scaling and multivariate analysis problems in
statistics;
genetics, geography, etc...

In this talk we look at the geometry of completions of **W**.