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Journal articles on the topic 'Geometric Mean'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Lim, Yongdo. "The inverse mean problem of geometric mean and contraharmonic means." Linear Algebra and its Applications 408 (October 2005): 221–29. http://dx.doi.org/10.1016/j.laa.2005.06.013.

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2

Zhang, Yan, Yu-Ming Chu, and Yun-Liang Jiang. "Sharp Geometric Mean Bounds for Neuman Means." Abstract and Applied Analysis 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/949815.

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We find the best possible constantsα1,α2,β1,β2∈[0,1/2]andα3,α4,β3,β4∈[1/2,1]such that the double inequalitiesG(α1a+(1-α1)b,α1b+(1-α1)a)<NAG(a,b)<G(β1a+(1-β1)b,β1b+(1-β1)a),G(α2a+(1-α2)b,α2b+(1-α2)a)<NGA(a,b)<G(β2a+(1-β2)b,β2b+(1-β2)a),Q(α3a+(1-α3)b,α3b+(1-α3)a)<NQA(a,b)<Q(β3a+(1-β3)b,β3b+(1-β3)a),Q(α4a+(1-α4)b,α4b+(1-α4)a)<NAQ(a,b)<Q(β4a+(1-β4)b,β4b+(1-β4)a)hold for alla,b>0witha≠b, whereG,A, andQare, respectively, the geometric, arithmetic, and quadratic means andNAG,NGA,NQA, andNAQare the Neuman means.

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3

Robitzsch, Alexander. "Extensions to Mean–Geometric Mean Linking." Mathematics 13, no. 1 (2024): 35. https://doi.org/10.3390/math13010035.

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Mean-geometric mean (MGM) linking is a widely used method for linking two groups within the two-parameter logistic (2PL) item response model. However, the presence of differential item functioning (DIF) can lead to biased parameter estimates using the traditional MGM method. To address this, alternative linking methods based on robust loss functions have been proposed. In this article, the conventional L2 loss function is compared with the L0.5 and L0 loss functions in MGM linking. Our results suggest that robust loss functions are preferable when dealing with outlying DIF effects, with the L0

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4

Qian, Wei-Mao, and Bo-Yong Long. "Sharp Bounds by the Generalized Logarithmic Mean for the Geometric Weighted Mean of the Geometric and Harmonic Means." Journal of Applied Mathematics 2012 (2012): 1–8. http://dx.doi.org/10.1155/2012/480689.

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5

Maynard, Philip. "89.46 Geometric-mean sequences." Mathematical Gazette 89, no. 515 (2005): 270–75. http://dx.doi.org/10.1017/s0025557200177812.

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6

Kim, Sejong, Hosoo Lee, and Yongdo Lim. "Geometric mean block matrices." Linear Algebra and its Applications 575 (August 2019): 299–313. http://dx.doi.org/10.1016/j.laa.2019.04.008.

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7

Jiang, Yi, William W. Hager, and Jian Li. "The geometric mean decomposition." Linear Algebra and its Applications 396 (February 2005): 373–84. http://dx.doi.org/10.1016/j.laa.2004.09.018.

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8

Somasundaram, S., S. S. Sandhya, and S. P. Viji. "On geometric mean graphs." International Mathematical Forum 10 (2015): 115–25. http://dx.doi.org/10.12988/imf.2015.412198.

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9

Ralha, Rui. "The geometric mean algorithm." Applied Mathematics and Computation 219, no. 4 (2012): 1607–15. http://dx.doi.org/10.1016/j.amc.2012.08.002.

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10

Li, Deqing, Wenyi Zeng, and Junhong Li. "Geometric Bonferroni Mean Operators." International Journal of Intelligent Systems 31, no. 12 (2016): 1181–97. http://dx.doi.org/10.1002/int.21822.

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11

MARKOWITZ, HARRY. "MEAN-VARIANCE APPROXIMATIONS TO THE GEOMETRIC MEAN." Annals of Financial Economics 07, no. 01 (2012): 1250001. http://dx.doi.org/10.1142/s2010495212500017.

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This paper uses two databases to test the ability of six functions of arithmetic mean and variance to approximate geometric mean return or, equivalently, Bernoulli's expected log utility. The two databases are: (1) a database of returns on frequently used asset classes, and (2) that of real returns on the equity markets of sixteen countries, 1900–2000. Three of the functions of arithmetic mean and variance do quite well, even for return series with large losses. The other three do less well.

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12

Long, Bo-Yong, and Yu-Ming Chu. "Optimal Power Mean Bounds for the Weighted Geometric Mean of Classical Means." Journal of Inequalities and Applications 2010 (2010): 1–6. http://dx.doi.org/10.1155/2010/905679.

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13

Kum, Sangho, and Yongdo Lim. "A Geometric Mean of Parameterized Arithmetic and Harmonic Means of Convex Functions." Abstract and Applied Analysis 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/836804.

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The notion of the geometric mean of two positive reals is extended by Ando (1978) to the case of positive semidefinite matricesAandB. Moreover, an interesting generalization of the geometric meanA # BofAandBto convex functions was introduced by Atteia and Raïssouli (2001) with a different viewpoint of convex analysis. The present work aims at providing a further development of the geometric mean of convex functions due to Atteia and Raïssouli (2001). A new algorithmic self-dual operator for convex functions named “the geometric mean of parameterized arithmetic and harmonic means of convex func

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14

Liu, Chunrong, and Siqi Liu. "Best possible inequalities between generalized logarithmic mean and weighted geometric mean of geometric, square-root, and root-square means." Journal of Mathematical Inequalities, no. 4 (2014): 899–914. http://dx.doi.org/10.7153/jmi-08-68.

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15

Nelsen, Roger B. "The Root Mean Square-Arithmetic Mean-Geometric Mean-Harmonic Mean Inequality." College Mathematics Journal 20, no. 3 (1989): 231. http://dx.doi.org/10.2307/2686772.

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16

Nelsen, Roger B. "The Root Mean Square-Arithmetic Mean-Geometric Mean-Harmonic Mean Inequality." College Mathematics Journal 20, no. 3 (1989): 231. http://dx.doi.org/10.1080/07468342.1989.11973236.

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17

Sağlam, Vedat. "Estimators Proposed by Geometric Mean, Harmonic Mean and Quadratic Mean." Science Journal of Applied Mathematics and Statistics 4, no. 3 (2016): 115. http://dx.doi.org/10.11648/j.sjams.20160403.15.

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18

Furuichi, Shigeru. "Operator inequalities among arithmetic mean, geometric mean and harmonic mean." Journal of Mathematical Inequalities, no. 3 (2014): 669–72. http://dx.doi.org/10.7153/jmi-08-49.

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19

Nam, Kyumin. "On a Mixed Arithmetic-Mean, Geometric-Mean, Harmonic-Mean Inequality." International Journal of Mathematics Trends and Technology 69, no. 5 (2023): 78–81. http://dx.doi.org/10.14445/22315373/ijmtt-v69i5p507.

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20

Farhadian, Reza, and Vadim Ponomarenko. "108.29 A geometric mean–arithmetic mean ratio limit." Mathematical Gazette 108, no. 572 (2024): 334–35. http://dx.doi.org/10.1017/mag.2024.104.

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21

Robitzsch, Alexander. "Comparing Different Specifications of Mean–Geometric Mean Linking." Foundations 5, no. 2 (2025): 20. https://doi.org/10.3390/foundations5020020.

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Mean–geometric mean (MGM) linking compares group differences on a latent variable θ within the two-parameter logistic (2PL) item response theory model. This article investigates three specifications of MGM linking that differ in the weighting of item difficulty differences: unweighted (UW), discrimination-weighted (DW), and precision-weighted (PW). These methods are evaluated under conditions where random DIF effects are present in either item difficulties or item intercepts. The three estimators are analyzed both analytically and through a simulation study. The PW method outperforms the other

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22

Kocic, Mikica. "Geometric mean of bimetric spacetimes." Classical and Quantum Gravity 38, no. 7 (2021): 075023. http://dx.doi.org/10.1088/1361-6382/abdf28.

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23

Nievergelt, Yves, and Achava Nakhash. "The Complex Geometric Mean: 10940." American Mathematical Monthly 110, no. 6 (2003): 546. http://dx.doi.org/10.2307/3647925.

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24

HE, XIAO-GANG, and A. ZEE. "GEOMETRIC MEAN NEUTRINO MASS RELATION." Modern Physics Letters A 22, no. 25n28 (2007): 2107–12. http://dx.doi.org/10.1142/s0217732307025352.

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Present experimental data from neutrino oscillations have provided much information about the neutrino mixing angles. Since neutrino oscillations only determine the mass squared differences [Formula: see text], the absolute values for neutrino masses mi, can not be determined using data just from oscillations. In this work we study implications on neutrino masses from a geometric mean mass relation [Formula: see text] which enables one to determined the absolute masses of the neutrinos. We find that the central values of the three neutrino masses and their 2σ errors to be m1 = (1.58 ± 0.18) me

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25

Mahajan, Sanjoy. "Don't demean the geometric mean." American Journal of Physics 87, no. 1 (2019): 75–77. http://dx.doi.org/10.1119/1.5082281.

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26

Dacheng Tao, Xuelong Li, Xindong Wu, and S. J. Maybank. "Geometric Mean for Subspace Selection." IEEE Transactions on Pattern Analysis and Machine Intelligence 31, no. 2 (2009): 260–74. http://dx.doi.org/10.1109/tpami.2008.70.

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27

Griffiths, Martin, and Des MacHale. "On arithmetic-geometric-mean polynomials." International Journal of Mathematical Education in Science and Technology 48, no. 1 (2016): 111–17. http://dx.doi.org/10.1080/0020739x.2016.1172740.

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28

de Camargo, André Pierro. "The geometric Mean Value Theorem." International Journal of Mathematical Education in Science and Technology 49, no. 4 (2017): 613–15. http://dx.doi.org/10.1080/0020739x.2017.1394503.

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29

Citron, Daniel, Adham Hurani, and Alaa Gnadrey. "The harmonic or geometric mean." ACM SIGARCH Computer Architecture News 34, no. 4 (2006): 18–25. http://dx.doi.org/10.1145/1186736.1186738.

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30

Bayat, M., and H. Teimoori. "Arithmetic–Geometric Mean determinantal identity." Linear Algebra and its Applications 435, no. 11 (2011): 2936–41. http://dx.doi.org/10.1016/j.laa.2011.05.031.

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31

Bracken, Paul. "An arithmetic-geometric mean inequality." Expositiones Mathematicae 19, no. 3 (2001): 273–79. http://dx.doi.org/10.1016/s0723-0869(01)80006-2.

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32

Gilbert, Andrew D., and Jacques Vanneste. "Geometric generalised Lagrangian-mean theories." Journal of Fluid Mechanics 839 (January 25, 2018): 95–134. http://dx.doi.org/10.1017/jfm.2017.913.

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Many fluctuation-driven phenomena in fluids can be analysed effectively using the generalised Lagrangian-mean (GLM) theory of Andrews & McIntyre (J. Fluid Mech., vol. 89, 1978, pp. 609–646) This finite-amplitude theory relies on particle-following averaging to incorporate the constraints imposed by the material conservation of certain quantities in inviscid regimes. Its original formulation, in terms of Cartesian coordinates, relies implicitly on an assumed Euclidean structure; as a result, it does not have a geometrically intrinsic, coordinate-free interpretation on curved manifolds, and

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33

Dung, Nguyen Tien. "Fractional geometric mean-reversion processes." Journal of Mathematical Analysis and Applications 380, no. 1 (2011): 396–402. http://dx.doi.org/10.1016/j.jmaa.2011.03.016.

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34

Pick, L., and B. Opic. "On the Geometric Mean Operator." Journal of Mathematical Analysis and Applications 183, no. 3 (1994): 652–62. http://dx.doi.org/10.1006/jmaa.1994.1172.

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35

Feng, Zixin, Teligeng Yun, Yu Zhou, Ruirui Zheng, and Jianjun He. "Kernel Geometric Mean Metric Learning." Applied Sciences 13, no. 21 (2023): 12047. http://dx.doi.org/10.3390/app132112047.

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Geometric mean metric learning (GMML) algorithm is a novel metric learning approach proposed recently. It has many advantages such as unconstrained convex objective function, closed form solution, faster computational speed, and interpretability over other existing metric learning technologies. However, addressing the nonlinear problem is not effective enough. The kernel method is an effective method to solve nonlinear problems. Therefore, a kernel geometric mean metric learning (KGMML) algorithm is proposed. The basic idea is to transform the input space into a high-dimensional feature space

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36

Wang, Jun-Li, Wei-Mao Qian, Zai-Yin He, and Yu-Ming Chu. "On Approximating the Toader Mean by Other Bivariate Means." Journal of Function Spaces 2019 (March 3, 2019): 1–7. http://dx.doi.org/10.1155/2019/6082413.

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37

Gan, Luyining, and Huajun Huang. "Order relations of the Wasserstein mean and the spectral geometric mean." Electronic Journal of Linear Algebra 40 (July 15, 2024): 491–505. http://dx.doi.org/10.13001/ela.2024.8669.

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On the space of positive definite matrices, several operator means are popular and have been studied extensively. In this paper, we investigate the near order and the Löwner order relations on the curves defined by the Wasserstein mean and the spectral geometric mean. We show that the near order $\preceq $ is stronger than the eigenvalue entrywise order and that $A\natural_t B \preceq A\diamond_t B$ for $t\in [0,1]$. We prove the monotonicity properties of the curves originated from the Wasserstein mean and the spectral geometric mean in terms of the near order. The Löwner order properties of

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38

Urmanin, Zbigniew. "86.43 Generalisation of the Arithmetic Mean: Geometric Mean: Harmonic Mean Inequality." Mathematical Gazette 86, no. 506 (2002): 293. http://dx.doi.org/10.2307/3621866.

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39

Yang, Zhen-Hang, and Jing-Feng Tian. "Optimal inequalities involving power-exponential mean, arithmetic mean and geometric mean." Journal of Mathematical Inequalities, no. 4 (2017): 1169–83. http://dx.doi.org/10.7153/jmi-2017-11-87.

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40

Chu, Yu-Ming, and Wei-Feng Xia. "Two Sharp Inequalities for Power Mean, Geometric Mean, and Harmonic Mean." Journal of Inequalities and Applications 2009, no. 1 (2009): 741923. http://dx.doi.org/10.1155/2009/741923.

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41

Głazowska, Dorota, and Janusz Matkowski. "An invariance of geometric mean with respect to Lagrangian means." Journal of Mathematical Analysis and Applications 331, no. 2 (2007): 1187–99. http://dx.doi.org/10.1016/j.jmaa.2006.09.005.

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42

Yang, Zhen-Hang. "Sharp bounds for Seiffert mean in terms of weighted power means of arithmetic mean and geometric mean." Mathematical Inequalities & Applications, no. 2 (2014): 499–511. http://dx.doi.org/10.7153/mia-17-37.

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43

Duong, Minh Thanh, Anh Vu Le, Cong Trinh Le, and Trung Hoa Dinh. "Revisiting Some Relationships Between the Weighted Spectral Mean and the Wasserstein Mean." Mathematics 13, no. 10 (2025): 1689. https://doi.org/10.3390/math13101689.

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In this paper, we introduce the 2-geometric mean and explore its connections with the spectral geometric mean and the Wasserstein mean for positive definite matrices. Additionally, we revisit and establish several inequalities involving these means in the context of the near order relation.

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44

Dorner, Bryan C. "More Meaning From the Geometric Mean." Mathematics Teacher 96, no. 2 (2003): 142–46. http://dx.doi.org/10.5951/mt.96.2.0142.

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We are all familiar with the average, or arithmetic mean, of two numbers. Less frequently used is the notion of the geometric mean. In “Geometric Meaning in the Geometric Mean Means More Meaningful Mathematics” in the March 2001 issue of the Mathematics Teacher, Matt E. Fluster shows how the geometric mean, s = _ab, of two positive numbers, a and b, can be used in a first-year algebra course to tie together geometric, algebraic, and computational investigations. In this article, I add a bit of history and an example suitable for more advanced courses. The example uses the geometric mean to com

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45

Schattschneider, Doris. "Proof without Words: The Arithmetic Mean-Geometric Mean Inequality." Mathematics Magazine 59, no. 1 (1986): 11. http://dx.doi.org/10.2307/2690011.

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46

Monhor, D. "The arithmetic-geometric mean and the elliptic mean error." Acta Geodaetica et Geophysica Hungarica 38, no. 1 (2003): 53–60. http://dx.doi.org/10.1556/ageod.38.2003.1.8.

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47

Kedlaya, Kiran. "Proof of a Mixed Arithmetic-Mean, Geometric-Mean Inequality." American Mathematical Monthly 101, no. 4 (1994): 355. http://dx.doi.org/10.2307/2975630.

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48

Alzer, Horst. "A Proof of the Arithmetic Mean-Geometric Mean Inequality." American Mathematical Monthly 103, no. 7 (1996): 585. http://dx.doi.org/10.2307/2974672.

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49

Levy, Haim. "Mean–Variance Analysis, the Geometric Mean, and Horizon Mismatch." Journal of Portfolio Management 50, no. 8 (2024): 161–81. http://dx.doi.org/10.3905/jpm.2024.50.8.161.

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50

Schattschneider, Doris. "Proof without words: The arithmetic mean-geometric mean inequality." Mathematics Magazine 59, no. 1 (1986): 11. http://dx.doi.org/10.1080/0025570x.1986.11977213.

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