Abstract
A matrix with zero diagonal is called a Euclidean distance matrix when the matrix values are measurements of distances between points in a Euclidean space. Because of data errors such a matrix may not be exactly Euclidean and it is desirable in many applications to find the best Euclidean matrix which approximates the non-Euclidean matrix. In this paper the problem is formulated as a smooth unconstrained minimization problem, for which rapid convergence can be obtained. Comparative numerical results are reported.
Highlights
1 Introduction Symmetric matrices with non-negative off-diagonal elements and zero diagonal elements arise as data in many experimental sciences
The aim of this paper is to study a new method for solving the Euclidean distance matrix problem and compare it with other older methods [ ]
An important application arises in the conformation of molecular structures from nuclear magnetic resonance data
Summary
Symmetric matrices with non-negative off-diagonal elements and zero diagonal elements arise as data in many experimental sciences This occurs when the values are measurements of squared distances between points in a Euclidean space (e.g. atoms, stars, cities). An important factor is the determination of the multiplicity of the zero eigenvalues, or alternatively the rank of the matrix at the solution. If this rank is known it is usually possible to solve the problem by conventional techniques. Semidefinite programming optimizes a linear function subject to a positive semidefinite matrix It is a convex programming problem since the objective and constraints are convex.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
