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||| ...

where i, j, and t are firm-, industry-, and time-specific subscripts. Yit is the output of firm i in year t in the form of total sales, and Y j is the corresponding geometric mean in industry j. xit denotes the use of factor z. We consider three factors of production, labor, capital, and material input costs. Labor input is measured by the total wage bill, capital by gross fixed assets, and mat...

this study was conducted to determine drought tolerance genotypes with superiority in different stressed environments. to screening quantitative indices of drought tolerance, genotypes of safflower (carthamus tinctorius l.) were tested in a complete randomized block design with three replications under two different water regimes (irrigated and rainfed). significant positive correlation was fou...

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.