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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 483624, 11 pages
Refinements of Kantorovich Inequality for Hermitian Matrices
School of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou, Chongqing 404000, China
Received 28 August 2012; Accepted 5 November 2012
Academic Editor: K. C. Sivakumar
Copyright © 2012 Feixiang Chen. 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.
- R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, UK, 1985.
- A. S. Householder, The Theory of Matrices in Numerical Analysis, Blaisdell, New York, NY, USA, 1964.
- S. Liu and H. Neudecker, “Several matrix Kantorovich-type inequalities,” Journal of Mathematical Analysis and Applications, vol. 197, no. 1, pp. 23–26, 1996.
- A. W. Marshall and I. Olkin, “Matrix versions of the Cauchy and Kantorovich inequalities,” Aequationes Mathematicae, vol. 40, no. 1, pp. 89–93, 1990.
- J. K. Baksalary and S. Puntanen, “Generalized matrix versions of the Cauchy-Schwarz and Kantorovich inequalities,” Aequationes Mathematicae, vol. 41, no. 1, pp. 103–110, 1991.
- S. S. Dragomir, “New inequalities of the Kantorovich type for bounded linear operators in Hilbert spaces,” Linear Algebra and its Applications, vol. 428, no. 11-12, pp. 2750–2760, 2008.
- P. G. Spain, “Operator versions of the Kantorovich inequality,” Proceedings of the American Mathematical Society, vol. 124, no. 9, pp. 2813–2819, 1996.
- S. Liu and H. Neudecker, “Kantorovich inequalities and efficiency comparisons for several classes of estimators in linear models,” Statistica Neerlandica, vol. 51, no. 3, pp. 345–355, 1997.
- P. Bloomfield and G. S. Watson, “The inefficiency of least squares,” Biometrika, vol. 62, pp. 121–128, 1975.
- L. V. Kantorovič, “Functional analysis and applied mathematics,” Uspekhi Matematicheskikh Nauk, vol. 3, no. 6(28), pp. 89–185, 1948 (Russian).
- C. G. Khatri and C. R. Rao, “Some extensions of the Kantorovich inequality and statistical applications,” Journal of Multivariate Analysis, vol. 11, no. 4, pp. 498–505, 1981.
- C. T. Lin, “Extrema of quadratic forms and statistical applications,” Communications in Statistics A, vol. 13, no. 12, pp. 1517–1520, 1984.
- A. Galántai, “A study of Auchmuty's error estimate,” Computers & Mathematics with Applications, vol. 42, no. 8-9, pp. 1093–1102, 2001.
- P. D. Robinson and A. J. Wathen, “Variational bounds on the entries of the inverse of a matrix,” IMA Journal of Numerical Analysis, vol. 12, no. 4, pp. 463–486, 1992.
- S. S. Dragomir, “A generalization of Grüss's inequality in inner product spaces and applications,” Journal of Mathematical Analysis and Applications, vol. 237, no. 1, pp. 74–82, 1999.
- S. S. Dragomir, “Some Grüss type inequalities in inner product spaces,” Journal of Inequalities in Pure and Applied Mathematics, vol. 4, no. 2, article 42, 2003.
- S. S. Dragomir, “On Bessel and Grüss inequalities for orthonormal families in inner product spaces,” Bulletin of the Australian Mathematical Society, vol. 69, no. 2, pp. 327–340, 2004.
- S. S. Dragomir, “Reverses of Schwarz, triangle and Bessel inequalities in inner product spaces,” Journal of Inequalities in Pure and Applied Mathematics, vol. 5, no. 3, article 76, 2004.
- S. S. Dragomir, “Reverses of the Schwarz inequality generalising a Klamkin-McLenaghan result,” Bulletin of the Australian Mathematical Society, vol. 73, no. 1, pp. 69–78, 2006.
- Z. Liu, L. Lu, and K. Wang, “On several matrix Kantorovich-type inequalities,” Journal of Inequalities and Applications, vol. 2010, Article ID 571629, 5 pages, 2010.