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=(wij)
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.