An Alternating Projection Algorithm for Computing the Nearest Euclidean Distance Matrix
- 1 October 1990
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Matrix Analysis and Applications
- Vol. 11 (4), 589-600
- https://doi.org/10.1137/0611042
Abstract
Recent extensions of von Neumann’s alternating projection algorithm permit an effective numerical approach to certain least squares problems subject to side conditions. This paper treats the problem of minimizing the distance from a given symmetric matrix to the class of Euclidean distance matrices; in dimension $n = 3$ we obtain the solution in closed form.
Keywords
This publication has 15 references indexed in Scilit:
- Approximation by matrices positive semidefinite on a subspaceLinear Algebra and its Applications, 1988
- A successive projection methodMathematical Programming, 1988
- The Young-Householder algorithm and the least squares multidimensional scaling of squared distancesJournal of Classification, 1987
- A Method for Finding Projections onto the Intersection of Convex Sets in Hilbert SpacesPublished by Springer Science and Business Media LLC ,1986
- Semi-Definite Matrix Constraints in OptimizationSIAM Journal on Control and Optimization, 1985
- Properties of Euclidean and non-Euclidean distance matricesLinear Algebra and its Applications, 1985
- The best Euclidian fit to a given distance matrix in prescribed dimensionsLinear Algebra and its Applications, 1985
- An Algorithm for Restricted Least Squares RegressionJournal of the American Statistical Association, 1983
- The theory and practice of distance geometryBulletin of Mathematical Biology, 1983
- Proximity maps for convex setsProceedings of the American Mathematical Society, 1959