Connections between the real positive semidefinite and distance matrix completion problems
نویسندگان
چکیده
منابع مشابه
Some Properties for the Euclidean Distance Matrix and Positive Semidefinite Matrix Completion Problems
The Euclidean distance matrix (EDM) completion problem and the positive semidefinite (PSD) matrix completion problem are considered in this paper. Approaches to determine the location of a point in a linear manifold are studied, which are based on a referential coordinate set and a distance vector whose components indicate the distances from the point to other points in the set. For a given ref...
متن کاملPolynomial Instances of the Positive Semidefinite and Euclidean Distance Matrix Completion Problems
Given an undirected graph G = (V; E) with node set V = 1; n], a subset S V and a rational vector a 2 Q SE , the positive semideenite matrix completion problem consists of determining whether there exists a real symmetric n n positive semideenite matrix X = (x ij) satisfying: x ii = a i (i 2 S) and x ij = a ij (ij 2 E). Similarly, the Euclidean distance matrix completion problem asks for the exi...
متن کاملSolving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming
Given a partial symmetric matrix A with only certain elements specified, the Euclidean distance matrix completion problem (EDMCP) is to find the unspecified elements of A that make A a Euclidean distance matrix (EDM). In this paper, we follow the successful approach in [20] and solve the EDMCP by generalizing the completion problem to allow for approximate completions. In particular, we introdu...
متن کاملDeterministic Symmetric Positive Semidefinite Matrix Completion
We consider the problem of recovering a symmetric, positive semidefinite (SPSD) matrix from a subset of its entries, possibly corrupted by noise. In contrast to previous matrix recovery work, we drop the assumption of a random sampling of entries in favor of a deterministic sampling of principal submatrices of the matrix. We develop a set of sufficient conditions for the recovery of a SPSD matr...
متن کاملEuclidean 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...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1995
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00096-a