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

The motivation of this work stems from the numerical approximation of boundedfunctions by polynomials satisfying the same bounds. The present contributionmakes use of the recent algebraic characterization found in [B. Despr\'es,Numer. Algorithms, 76(3), (2017)] and [B. Despr\'es and M. Herda, Numer.Algorithms, 77(1), (2018)] where an interpretation of monovariate polynomialswith two bounds is provided in terms of a quaternion algebra and the Eulerfour-squares formulas. Thanks to this structure, we generate a new nonlinearprojection algorithm onto the set of polynomials with two bounds. The numericalanalysis of the method provides theoretical error estimates showing stabilityand continuity of the projection. Some numerical tests illustrate this novelalgorithm for constrained polynomial approximation.

A projection algorithm on the set of polynomials with two bounds