English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we show that the weighted Bernstein-Walsh inequality inlogarithmic potential theory is sharp up to some new universal constant,provided that the external field is given by a logarithmic potential. Our maintool for such results is a new technique of discretization of logarithmicpotentials, where we take the same starting point as in earlier work of Totikand of Levin \& Lubinsky, but add an important new ingredient, namely some newmean value property for the cumulative distribution function of the underlyingmeasure. As an application, we revisit the work of Beckermann \& Kuijlaars onthe superlinear convergence of conjugate gradients. These authors havedetermined the asymptotic convergence factor for sequences of systems of linearequations with an asymptotic eigenvalue distribution. There was some numericalevidence to let conjecture that the integral mean of Green functions occurringin their work should also allow to give inequalities for the rate ofconvergence if one makes a suitable link between measures and the eigenvaluesof a single matrix of coefficients. We prove this conjecture , at least for aclass of measures which is of particular interest for applications.

On the sharpness of the weighted Bernstein-Walsh inequality, with applications to the superlinear convergence of conjugate gradients