Jack-Kang Chan, "A novel interpretation of least squares solution", International Journal of Mathematics and Mathematical Sciences, vol. 15, Article ID 893536, 6 pages, 1992. https://doi.org/10.1155/S016117129200005X
A novel interpretation of least squares solution
We show that the well-known least squares (LS) solution of an overdetermined system of linear equations is a convex combination of all the non-trivial solutions weighed by the squares of the corresponding denominator determinants of the Cramer's rule. This Least Squares Decomposition (LSD) gives an alternate statistical interpretation of least squares, as well as another geometric meaning. Furthermore, when the singular values of the matrix of the overdetermined system are not small, the LSD may be able to provide flexible solutions. As an illustration, we apply the LSD to interpret the LS-solution in the problem of source localization.
Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.