Results 231 to 240 of about 18,915 (259)

Arithmetic-geometric means of positive matrices

Mathematical Proceedings of the Cambridge Philosophical Society, 1987
AbstractWe prove the existence of unique limits and establish inequalities for matrix generalizations of the arithmetic–geometric mean of Lagrange and Gauss. For example, for a matrix A = (aij) with positive elements aij, define (contrary to custom) A½ elementwise by [A½]ij = (aij)½.
Cohen, Joel E., Nussbaum, Roger D.
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The arithmetic-geometric mean and the elliptic mean error

Acta Geodaetica et Geophysica Hungarica, 2003
Without any special term, the mathematical definition of a measuring index for reliability of geodetic point was given by Lajos Homorodi. For this index, the term of the elliptic mean error was proposed by the author of the present paper and it was shown that the elliptic mean error is beneficial to the being for characterizing the reliability of ...
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A refinement of the arithmetic–geometric mean inequality

International Journal of Mathematical Education in Science and Technology, 2014
In the short note, the authors present a refinement of the well-known arithmetic–geometric mean inequality by virtue of Taylor's theorem.
Limin Zou, Yi Huang
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Remarks on the matrix arithmetic–geometric mean inequality

Acta Scientiarum Mathematicarum
The author proves among others: (1) Let \(A\) and \(B\) be positive definite matrices. Then for every unitarily invariant norm \[ \left\vert {\left\Vert A^{\frac{1}{2}}B^{\frac{1}{2}} \right\Vert} \right\vert \leqslant \left\vert {\left\Vert {(AB)}^{\frac{1}{2}}+{(BA)}^{\frac{1}{2}} \right\Vert} \right\vert \leqslant (1/2) \left\vert {\left\Vert {A + B}
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Higher genus arithmetic-geometric means

The Ramanujan Journal, 2007
For any two complex numbers, one can define as usual their arithmetic-geometric mean. Due to the ambiguity of the square root, this is a multi-valued function. Given one value, Gauss determined all its values and moreover showed that they are closely related to certain elliptic integrals.
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Arithmetic-geometric means for electrical energies

Proceedings of the IEEE, 1980
The paper indicates an important arithmetic-geometric relation for the behavior of linear passive reciprocal n-ports. The active energies dissipated in the unit time interval in any linear passive time invariant reciprocal resistive system satisfy the inequalities P 1 + P 2 ≥ 2P 0 √P 1 P 2 ≥ P 0 where P 1 = (V 1 , I 1 ), P 2 = (V 2 , I 2 ), P 0 = (V 1 ,
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A Generalized Arithmetic-Geometric Mean

SIAM Review, 1983
D. Borwein, P. B. Borwein
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The arithmetic mean of what? A Cautionary Tale about the Use of the Geometric Mean as a Measure of Fitness

Biology and Philosophy, 2022
Pierrick Bourrat, Peter Takacs, Bourrat Pierrick   +2 more
exaly  

A Generalized Arithmetic-Geometric Mean

SIAM Review, 1984
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A generalized arithmetic-geometric mean-type inequality of measurable operator

Linear and Multilinear Algebra, 2023
Cheng Yan, Sun Shuoxi
exaly