plenary talk at Western Canada Linear Algebra Meeting, WCLAM (Western Canada Linear Algebra Meeting) held at the University of Manitoba, Winnipeg on May 26,27, 2000 (Friday and Saturday).

(The Abstract (text file):; the presentation (ps file))

This talk is based on several papers; principally, on the papers dealing with 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.