Bisection (of a real interval) is a well known algorithm to compute eigenvalues of symmetric matrices. Given an initial interval [a, b], convergence to an eigenvalue which has size much smaller than a or b may be made considerably faster if one replaces the usual arithmetic mean (of the end points of the current interval) with the geometric mean. Exploring this idea, we have implemented geometr...

An attractive candidate for the geometric mean of m positive definite matrices A1, . . . , Am is their Riemannian barycentre G. One of its important properties, monotonicity in the m arguments, has been established recently by J. Lawson and Y. Lim. We give a much simpler proof of this result, and prove some other inequalities. One of these says that, for every unitarily invariant norm, |||G||| ...

abstract the saturated hydraulic conductivity (ks) is an important physical property of soil. the direct measurement of this property in soils is a difficult and time consuming process. pedotransfer functions (ptfs) provide an alternative by estimating soil parameters from more readily available soil data. the objective of this study is to determine effective factors on soil hydraulic conductiv...

For a,b > 0 with a = b , let P = (a− b)/(4arctana/b−π) , A = (a+ b)/2 , G = √ ab denote the Seiffert mean, arithmetic mean, geometric mean of a and b , respectively. In this paper, we present new sharp bounds for Seiffert P in terms of weighted power means of arithmetic mean A and geometric mean G : ( 2 3 A p1 + 3 G p1 )1/p1 < P < ( 2 3 A p2 + 3 G p2 )1/p2 , where p1 = 4/5 and p2 = logπ/2 (3/2)...

In this short note, we present a refinement of the logarithmic-geometric mean inequality. As an application of our result, we obtain an operator inequality associated with geometric and logarithmic means.

Epidemiological studies have reported process-specific elevated prevalence of beryllium sensitization (BeS) and chronic beryllium disease (CBD) among workers. However, exposure-response relationships have been inconsistent, possibly due to incomplete characterization of many biologically relevant aspects of exposure, including particle size. In 1999, two surveys were conducted 3-5 months apart ...

It is well-known that for Hilbert space linear operators 0 ≤ A and 0 ≤ C, inequality C ≤ A does not imply C ≤ A. We introduce a strong order relation 0 ≤ B≪ A, which guarantees that C ≤ BAB for all 0 ≤ C ≤ B, and that C ≤ A when B commutes with A. Connections of this approach with the arithmetic-geometric mean inequality of Bhatia–Kittaneh as well as the Kantorovich constant of A are mentioned.

T his article describes an important improvement in the calculation of the Consumer Price Index (CPI). The Bureau of Labor Statistics plans to use a new geometric mean formula for calculating most of the basic components of the Consumer Price Index for all Urban Consumers (CPI-U) and the Consumer Price Index for Urban Wage Earners and Clerical Workers (CPI-W). This change will become effective ...