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1 sty 2011 · 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 an EDM.We...
3.1] A Euclidean distance matrix, an EDM in RN×N +, is an exhaustive table of distance-square dij between points taken by pair from a list of N points {xℓ, ℓ=1...N} in Rn; the squared metric, the measure of distance-square: dij = kxi − xjk 2 2, hxi − xj, xi − xji (1037)
For papers on the Euclidean distance ma-trix completion problem and the related semidefinite completion problem, see the classic paper on semidefinite completion [67], and follow-up papers [19] and [78]; also see [88] on the topic of the complexity of these completion problems.
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.
Molecular conformation problem. We measure the distances between the atoms, The distances are given as intervals, and some are missing, How do we reconstruct the molecule? Density map and structure of a molecule [10.7554/elife.01345] Euclidean Distance Matrix. Consider a set of n points X 2 Rd n,
Title Euclidean Distance Matrix Completion Tools Description Implements various general algorithms to estimate missing elements of a Euclidean (squared) distance matrix. Includes optimization methods based on semi-definite programming found in Alfakih, Khadani, and Wolkowicz (1999)<doi:10.1023/A:1008655427845>, a non-convex position formula-
The nearest (or approximate) Euclidean distance matrix problem is to find a Euclidean distance matrix, EDM, that is nearest in the Frobenius norm to the matrix A, when the free variables are discounted. In this paper we introduce two algorithms: one for the exact completion problem and one for the approximate completion problem.
