Related papers: Bounds of the logarithmic mean

We prove majorization inequalities for different means of positive definite matrices. These include the Cartan mean (the Karcher mean), the log Euclidean mean, the Wasserstein mean and the power mean.

We apply polynomial techniques (linear programming) to obtain lower and upper bounds on the covering radius of spherical designs as function of their dimension, strength, and cardinality. In terms of inner products we improve the lower…

In the paper, some lower bounds for polygamma functions are refined.

Consider a meromorphic connection on P^1 over a p-adic field. In many cases, such as those arising from Picard-Fuchs equations or Gauss-Manin connections, this connection admits a Frobenius structure defined over a suitable rigid analytic…

In this paper, we establish some new integral inequalities for for m- and (alpha,m)-logarithmically convex functions.

We obtain new mean value theorems for exponential sums with very smooth numbers, which provide a power saving against the trivial bound in region where previous bounds do not apply.

In the paper, the authors establish an inequality involving exponential functions and sums, introduce a ratio of many gamma functions, discuss properties, including monotonicity, logarithmic convexity, (logarithmically) complete…

We establish an inequality of different metrics for algebraic polynomials.

We show how positive unital linear maps can be used to obtain lower bounds for the maximum distance between the eigenvalues of two normal matrices. Some related bounds for the spread and condition number of Hermitian matrices are also…

In this expository and survey paper, along one of main lines of bounding the ratio of two gamma functions, we look back and analyse some inequalities, several complete monotonicity of functions involving ratios of two gamma or $q$-gamma…

We consider the problem of estimating the spectral norm of a matrix using only matrix-vector products. We propose a new Counterbalance estimator that provides upper bounds on the norm and derive probabilistic guarantees on its…

We give a bound for the number of real solutions to systems of n polynomials in n variables, where the monomials appearing in different polynomials are distinct. This bound is smaller than the fewnomial bound if this structure of the…

We give a refined Young inequality which generalizes the inequality by Zou--Jiang. We also show the upper bound for the logarithmic mean by the use of the weighted geometric mean and the weighted arithmetic mean. Furthermore, we show some…

We study generalized means whose domain may contain unbounded sets as well. We investigate usual properties of this type of means and also new attributes that regard for such means only. We examine how a mean defined on bounded sets can be…

This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…

We present inequalities related to generalized matrix function for positive semidefinite block matrices. We introduce partial generalized matrix functions corresponding to partial traces, and then provide a unified extension of the recent…

In the paper, the authors review origins, motivations, and generalizations of a series of inequalities involving several exponential functions and sums, establish three new inequalities involving finite exponential functions and sums by…

Generalized Frobenius powers of an ideal were introduced in work of Hern\'andez, Teixeira, and Witt as characteristic-dependent analogs of test ideals. However, little is known about the Frobenius powers and critical exponents of specific…

We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and…

In this paper, we present some new inequalities for the gamma function. The main tools are the multiple-correction method developed in our previous works, and a generalized Mortici's lemma.