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Cauchy–Schwarz and Kantorovich type inequalities for scalar and matrix moment sequences

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Abstract

First we present various scalar inequalities that extends the classical Cauchy–Schwarz and Kantorovich inequalities. Some of these extensions are based on the moment problem and the Hölder and Minkowski inequalities. These results are then extended to the matrix case. Many well-known inequalities are recovered ans new ones are obtained.

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Authors and Affiliations

  1. Laboratoire Paul Painlevé, UMR CNRS 8524, UFR de Mathématiques Pures et Appliquées,, Université des Sciences et Technologies de Lille, 59655, Villeneuve d'Ascq Cedex, France

    C. Brezinski

  2. Dpto. de Computación, Facultad de Ciencias, Universidad Central de Venezuela, Ap. 47002, Caracas, 1041-A, Venezuela

    M. Raydan

Authors
  1. C. Brezinski
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  2. M. Raydan
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Correspondence to C. Brezinski.

Additional information

Communicated by Jesus Carnicer and Juan Manuel Peña

Dedicated with friendship to Mariano Gasca at the occasion of his 60th birthday

M. Raydan: This author was partially supported by the Scientific Computing Center at UCV.

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Brezinski, C., Raydan, M. Cauchy–Schwarz and Kantorovich type inequalities for scalar and matrix moment sequences. Adv Comput Math 26, 71–80 (2007). https://doi.org/10.1007/s10444-004-7646-8

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  • DOI: https://doi.org/10.1007/s10444-004-7646-8

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