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/

Zendy Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

We study linear problems defined on tensor products of Hilbert spaces with anadditional (anti-) symmetry property. We construct a linear algorithm that usesfinitely many continuous linear functionals and show an explicit formula forits worst case error in terms of the singular values of the univariate problem.Moreover, we show that this algorithm is optimal with respect to a wide classof algorithms and investigate its complexity. We clarify the influence ofdifferent (anti-) symmetry conditions on the complexity, compared to theclassical unrestricted problem. In particular, for symmetric problems we givecharacterizations for polynomial tractability and strong polynomialtractability in terms of the amount of the assumed symmetry. Finally, we applyour results to the approximation problem of solutions of the electronicSchr\"odinger equation.

The Complexity of Linear Tensor Product Problems in (Anti-) Symmetric Hilbert Spaces