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Buzano's inequality and bounds for roots of algebraic equations


Authors: Masatoshi Fujii and Fumio Kubo
Journal: Proc. Amer. Math. Soc. 117 (1993), 359-361
MSC: Primary 47A30; Secondary 15A63, 26D99, 47A99
DOI: https://doi.org/10.1090/S0002-9939-1993-1088441-X
MathSciNet review: 1088441
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Abstract: A new bound for roots of algebraic equations will be given as a consequence of an inequality due to Buzano.


References [Enhancements On Off] (What's this?)

  • [1] M. L. Buzano, Generalizzatione della diseguaglianza di Cauchy-Schwarz, Rend. Sem. Mat. Univ. e Politech. Trimo 31 (1971/73), 405-409. MR 0344857 (49:9596)
  • [2] K. R. Davidson and J. A. R. Holbrook, Numerical radii of zero-one matrices, Michigan Math. J. 35 (1988), 261-267. MR 959273 (89k:47007)
  • [3] M. Fujii and F. Kubo, Operator norms as bounds for roots of algebraic equations, Proc. Japan Acad. Sci. 49 (1973), 805-808. MR 0364310 (51:565)
  • [4] R. A. Horn and C. A. Johnson, Matrix analysis, Cambridge Univ. Press, Cambridge, 1985. MR 832183 (87e:15001)
  • [5] M. Marden, The geometry of zeros of a polynomial in a complex variable, 2nd ed., Math. Survey, vol. 3, Amer. Math. Soc., Providence, RI, 1960. MR 0031114 (11:101i)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1993-1088441-X
Keywords: Numerical radius companion matrix, Schwarz's inequality bound for roots
Article copyright: © Copyright 1993 American Mathematical Society

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