Summary
It is shown that the approximate null vector of a perturbed degenerate matrix behaves linearly under column scaling up to second order terms in the perturbation. This result has important consequences for an estimation technique known to numerical analysts as total least squares and to statisticians as latent root regression.
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References
Golub, G., Van Loan, C.: An analysis of the Total Least Squares Problem. SIAM J. Numer. Anal.6, 883–893 (1980)
Stewart, G.W.: Introduction to Matrix Computations. New York: Academic Press 1974
Stewart, G.W.: Rank degeneracy. SIAM J. Scient. Stat. Comput. (to appear)
Webster, J., Gunst, R., Mason, R.: Latent root regression analysis. Technometrics16, 513–522 (1974)
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Dedicated to F.L. Bauer on the occasion of his 60th birthday
Department of Computer Science and Institute for Physical Science and Technology, University of Maryland at College Park. This work was done while the author was at the Scientific Computing Division of the National Bureau of Standards
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Stewart, G.W. On the invariance of perturbed null vectors under column scaling. Numer. Math. 44, 61–65 (1984). https://doi.org/10.1007/BF01389755
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DOI: https://doi.org/10.1007/BF01389755