talk at Seventh SIAM Conference on Applied Linear Algebra, Oct. 23-26, 2000.

In progress (The Abstract (text file):; the presentation (ps file))
An expanded version of this talk will be given in the dept of O.R. at the University of North Carolina , Chapel Hill, on Thursday Oct 26.

This talk is based on several papers; principally, on the papers dealing with completion problems. The paper (in progress)
New Semidefinite Programming Model for Large Sparse Euclidean Distance Matrix Completion Problems.
The paper
Positive definite completions of partial {H}ermitian matrices (GRONE, B. and JOHNSON, C.R. and MARQUES de SA, E. and WOLKOWICZ, H.) presents a characterization for completion using chordality of graphs;
while the two papers:
AN INTERIOR-POINT METHOD FOR APPROXIMATE POSITIVE SEMIDEFINITE COMPLETIONS and
Solving Euclidean distance matrix completion problems via semidefinite programming
present primal-dual interior-point methods for solving approximate completion problems. A summary of these results is presented in
Matrix Completion Problems, in the Handbook of Semidefinite Programming, Kluwer Academic, 2000.