Results 11 to 20 of about 4,387,980 (294)
Further Improved Weighted Arithmetic-Geometric Operator Mean Inequalities
Mathematics, 2019 The main purpose of this paper is to present some weighted arithmetic-geometric operator mean inequalities. These inequalities are refinements and generalizations of the corresponding results.
Jianming Xue, Xingkai Hu
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The matrix arithmetic–geometric mean inequality revisited
Linear Algebra and its Applications, 2008 The authors survey the developments of a matrix version of the arithmetic-geometric mean inequality, and discuss other closely related matters. The article can also serve as introduction to the basic ideas and typical problems of the flourishing subject of matrix inequalities.
Bhatia, Rajendra, Kittaneh, Fuad
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Hyperelliptic integrals and generalized arithmetic–geometric mean [PDF]
The Ramanujan Journal, 2012 Consider \(d=2g+2\) real numbers (there is ultimately no real loss of generality in assuming that \(d\) is even ...
Spandaw, J. (author) +1 more
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Notes on matrix arithmetic–geometric mean inequalities
Linear Algebra and its Applications, 2000 The authors prove that a unitarily invariant norm of 4AB does not exceed that of \((A+B)^2\), for positive semi-definite matrices \(A\), \(B\). Connections with some other matrix arithmetic-geometric mean inequalities and trace inequalities are discussed.
Bhatia, Rajendra, Kittaneh, Fuad
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On a Mixed Arithmetic-Mean, Geometric-Mean, Harmonic-Mean Inequality [PDF]
, 2023 In 1992, F. Holland conjectured a mixed arithmetic-mean, geometric-mean inequality and it was proved by K. Kedlaya in 1994. In this note, we provide more extended inequality: a mixed arithmetic-mean, geometric-mean, harmonic-mean ...
Kyumin Nam
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On the arithmetic-geometric mean inequality [PDF]
Journal of Mathematical Inequalities, 2021 Summary: In this article, we present a new treatment of the arithmetic-geometric mean inequality and its siblings, the Heinz and the Young inequalities. New refinements via calculus computations and convex analysis are presented and a new Heinz-type inequality is presented for any symmetric operator mean.
Sababheh, Mohammad +3 more
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A generalization of the arithmetic-geometric means inequality [PDF]
Proceedings of the American Mathematical Society, 1976 It is shown that the arithmetic mean of x 1
Fink, A. M., Jodeit, Max jun.
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Matrix Arithmetic-Geometric Mean and the Computation of the Logarithm [PDF]
SIAM Journal on Matrix Analysis and Applications, 2016 Summary: We investigate the stability of the matrix arithmetic-geometric mean (AGM) iteration. We show that the classical formulation of this iteration may be not stable (a necessary and sufficient condition for its stability is given) and investigate the numerical properties of alternative formulations. It turns out that the so-called Legendre form is
João R. Cardoso, Rui Ralha
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On An Inequality of Diananda [PDF]
, 2002 We consider certain refinements of the arithmetic and geometric means, the results generalize an inequality of P ...
Gao, Peng
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A Generalization of the Inequality of the Arithmetic-Geometric Means [PDF]
Proceedings of the Glasgow Mathematical Association, 1956 The main result in this paper, contained in Theorem 1, is a generalisation of the inequality of the arithmetic-geometric means. A result of a similar character has been proved by Siegel (2). The present result gives an improvement in the inequality in the case when the variables involved are not all distinct, whereas Siegel's result does not.
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