Stronger forms of a class of inequalities of G. Pólya-G. Szegö, and L. V. Kantorovich
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- by J. B. Diaz and F. T. Metcalf PDF
- Bull. Amer. Math. Soc. 69 (1963), 415-418
References
- F. L. Bauer, A further generalization of the Kantorovič inequality, Numer. Math. 3 (1961), 117–119. MR 122824, DOI 10.1007/BF01386009
- F. L. Bauer and A. S. Householder, Some inequalities involving the euclidean condition of a matrix, Numer. Math. 2 (1960), 308–311. MR 116027, DOI 10.1007/BF01386231
- Edwin F. Beckenbach and Richard Bellman, Inequalities, Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 30, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. MR 0158038, DOI 10.1007/978-3-642-64971-4
- G. T. Cargo and O. Shisha, Bounds on ratios of means, J. Res. Nat. Bur. Standards Sect. B 66B (1962), 169–170. MR 147595, DOI 10.6028/jres.066B.018
- G. S. Watson, Serial correlation in regression analysis. I, Biometrika 42 (1955), 327–341. MR 73096, DOI 10.1093/biomet/42.3-4.327
- Werner Greub and Werner Rheinboldt, On a generalization of an inequality of L. V. Kantorovich, Proc. Amer. Math. Soc. 10 (1959), 407–415. MR 105028, DOI 10.1090/S0002-9939-1959-0105028-3
- Peter Henrici, Two remarks on the Kantorovich inequality, Amer. Math. Monthly 68 (1961), 904–906. MR 136623, DOI 10.2307/2311698
- A. S. Householder and F. L. Bauer, On certain iterative methods for solving linear systems, Numer. Math. 2 (1960), 55–59. MR 116464, DOI 10.1007/BF01386209 9. L. V. Kantorovich, Funktsionalnii analyz i prikladnaya matematika, Uspehi Mat. Nauk 3 (1948), 89-185; in particular pp. 142-144 (also translated from the Russian by C. D. Benster, Nat. Bur. Standards Report No. 1509, March 7, 1952; in particular pp. 106-109). 10. J. Kürschák, Math. Phys. Lapok 23 (1914), 378. 11. Marvin Marcus and A. H. Cayford, Further results on the Kantorovich inequality, Notices Amer. Math. Soc. 9 (1962), 300.
- Marvin Marcus and N. A. Khan, Some generalizations of Kantorovich’s inequality, Portugal. Math. 20 (1961), 33–38. MR 130261
- Morris Newman, Kantorovich’s inequality, J. Res. Nat. Bur. Standards Sect. B 64B (1960), 33–34. MR 109157, DOI 10.6028/jres.064B.003 14. G. Pólya and G. Szegö, Aufgaben und Lehrsätze aus der Analysis, Vol. 1, Springer, Berlin, 1925; in particular pp. 57, 213-214.
- Andreas H. Schopf, On the Kantorovich inequality, Numer. Math. 2 (1960), 344–346. MR 113892, DOI 10.1007/BF01386235 16. P. Schweitzer, Egy egyenlötlenség az aritmetikai középértékröl (An inequality concerning the arithmetic mean), Math. Phys. Lapok 23 (1914), 257-261.
- G. Strang, On the Kantorovich inequality, Proc. Amer. Math. Soc. 11 (1960), 468. MR 112046, DOI 10.1090/S0002-9939-1960-0112046-6
Additional Information
- Journal: Bull. Amer. Math. Soc. 69 (1963), 415-418
- DOI: https://doi.org/10.1090/S0002-9904-1963-10953-2
- MathSciNet review: 0146324