Sensor Network Localization, Euclidean Distance Matrix completions, and graph realization

Euclidean Distance Matrices, Semidefinite Programming, and Sensor Network Localization

The fundamental problem of distance geometry, F P DG , involves the characterization and study of sets of points based only on given values of (some of) the distances between pairs of points. This problem has a wide range of applications in various areas of mathematics, physics, chemistry, and engineering. Euclidean Distance Matrices, EDM , play an important role in F P DG . They use the square...

Euclidean distance matrix completion problems

A Euclidean distance matrix is one in which the (i, j) entry specifies the squared distance between particle i and particle j. Given a partially-specified symmetric matrix A with zero diagonal, the Euclidean distance matrix completion problem (EDMCP) is to determine the unspecified entries to make A a Euclidean distance matrix. We survey three different approaches to solving the EDMCP.We advoca...

A matrix Euclidean algorithm for minimal partial realization

A Matrix Euclidean Algorithm induced by State Space Realization

An eecient algorithm is developed for determining the greatest common left divisor (GCLD) of two polynomial matrices. Knowing this divisor allows for several immediate applications: In coding theory, a noncatastrophic convolutional encoder can be derived from an arbitrary one. In systems theory, irreducible matrix fraction descriptions of transfer function matrices can be found. In linear algeb...

On Least Squares Euclidean Distance Matrix Approximation and Completion

The Euclidean distance matrix approximation problem as well as the completion problem have received a lot of attention in recent years because of their many important applications. In contrast to the many interesting but often sophisticated algorithms proposed in the literature, this paper offers a relatively straightforward procedure that can tackle both problems by the same framework. The loc...