Abstract
Based on the singular value decomposition, we obtain both additive and multiplicative perturbation bounds for the orthogonal projection, which improve some existing results. Furthermore, the Q-norm bounds for additive and multiplicative perturbations of the orthogonal projection are also given.
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References
Bhatia, R.: Matrix Analysis. Springer, New York (1997)
Chen, X.S., Li, W.: Relative perturbation bounds for the subunitary polar factor under unitarily invariant norms. Adv. Math. 35, 178–184 (2006) (in Chinese)
Li, W.: Some new perturbation bounds for subunitary polar factors. Acta Math. Sinica (Eng. Ser) 21(6), 1515–1520 (2005)
Stewart, G.W.: On the perturbation of the pseudo-inverse, projections and linear squares problems. SIAM Rev. 19, 634–662 (1977)
Sun, J.: Matrix Perturbation Analysis, 2nd edn. Science Press, Beijing (2001) (in Chinese)
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The authors would like to thank the referee for his/her helpful comments.
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W. Li was supported in part by National Natural Science Foundations of China (No. 10671077, 10971075), Research Fund for the Doctoral Program of Higher Education of China (No. 20104407110002) and Guangdong Provincial Natural Science Foundations (No. 9151063101000021 and 06025061), P.R. China.
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Li, B., Li, W. & Cui, L. New bounds for perturbation of the orthogonal projection. Calcolo 50, 69–78 (2013). https://doi.org/10.1007/s10092-012-0058-0
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DOI: https://doi.org/10.1007/s10092-012-0058-0