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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We study the efficient construction of good polynomial lattice rules, whichare special instances of quasi-Monte Carlo (QMC) methods. The integration rulesobtained are of particular interest for the approximation of multivariateintegrals in weighted Walsh spaces. In particular, we study a constructionalgorithm which assembles the components of the generating vector, which is inthis case a vector of polynomials over a finite field, of the polynomiallattice rule in a component-wise fashion. We show that the constructed QMCrules achieve the almost optimal error convergence order in the function spacesunder consideration and prove that the obtained error bounds can, under certainconditions on the involved weights, be made independent of the dimension. Wealso demonstrate that our alternative component-by-component construction,which is independent of the underlying smoothness of the function space, can beimplemented relatively easily in a fast manner. Numerical experiments confirmour theoretical findings.

Construction of good polynomial lattice rules in weighted Walsh spaces by an alternative component-by-component construction