Can I read Universal rigidity of bar frameworks in general position: a Euclidean distance matrix approach on EtoBox?

Universal rigidity of bar frameworks in general position: a Euclidean distance matrix approach by Alfakih, A. Y. is a scholarly article available to read on EtoBox.

What is Universal rigidity of bar frameworks in general position: a Euclidean distance matrix approach about?

A configuration p in r-dimensional Euclidean space is a finite collection of labeled points p^1,p^2,...,p^n in R^r that affinely span R^r. Each configuration p defines a Euclidean distance matrix D_p = (d_ij) = (||p^i-p^j||^2), where ||.|| denotes the Euclidean norm. A fundamental problem in distance geometry is to find out whether or not, a given proper subset of the entries of D_p suffices to uniquely determine the entire matrix D_p. This problem is known as the universal rigidity problem of bar frameworks. In this chapter, we present a unified approach for the universal rigidity of bar frameworks, based on Euclidean distance matrices (EDMs), or equivalently, on projected Gram matrices. This approach makes the universal rigidity problem amenable to semi-definite programming methodology. Using this approach, we survey some recently obtained results and their proofs, emphasizing the case where the points p^1,...,p^n are in general position.

Author

Alfakih, A. Y.

Published

2012

Language

EN