Euclidean distances and least squares problems for a given set of vectors

Authors:
Xiao-Wen Chang;Christopher C. Paige
Affiliations:
School of Computer Science, McGill University, Montreal, Quebec, Canada, H3A 2A7;School of Computer Science, McGill University, Montreal, Quebec, Canada, H3A 2A7
Venue:
Applied Numerical Mathematics
Year:
2007

Citing 3
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Abstract

Given an mxn matrix A, n Euclidean distances, those from each column to the space spanned by the remaining columns of A, are considered. An elegant relationship between A, these Euclidean distances, and the solutions of n simple linear least squares problems arising from A is derived. When A has full column rank, from this a useful expression for these Euclidean distances is immediately obtained. The theory is then used to greatly improve the efficiency of an algorithm used in communications.