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 Plus

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

Zendy Tools

Zendy Open

In several applications, such as \tsc{weno} interpolation and reconstruction[Shu C.W.: SIAM Rev. 51 (2009) 82--126], we are interested in the analyticalexpression of the weight-functions which allow the representation of theapproximating function on a given stencil (Chebyshev-system) as the weightedcombination of the corresponding approximating functions on substencils(Chebyshev-subsystems). We show that the weight-functions in suchrepresentations [M\"uhlbach G.: Num. Math. 31 (1978) 97--110] can be generatedby a general recurrence relation based on the existence of a 1-levelsubdivision rule. As an example of application we apply this recurrence to thecomputation of the weight-functions for Lagrange interpolation [Carlini E.,Ferretti R., Russo G.: SIAM J. Sci. Comp. 27 (2005) 1071--1091] for a generalsubdivision of the stencil ${x_{i-M_-},...,x_{i+M_+}}$ of $M+1:=M_-+M_++1$distinct ordered points into $K_\mathrm{s}+1\leq M:=M_-+M_+>1$ (Neville)substencils ${x_{i-M_-+k_\mathrm{s}},...,x_{i+M_+-K_\mathrm{s}+k_\mathrm{s}}}$($k_\mathrm{s}\in{0,...,K_\mathrm{s}}$) all containing the same number of$M-K_\mathrm{s}+1$ points but each shifted by 1 cell with respect to itsneighbour, and give a general proof for the conditions of positivity of theweight-functions (implying convexity of the combination), extending previousresults obtained for particular stencils and subdvisions [Liu Y.Y., Shu C.W.,Zhang M.P.: Acta Math. Appl. Sinica 25 (2009) 503--538]. Finally, we apply therecurrence relation to the representation by combination of substencils ofderivatives of arbitrary order of the Lagrange interpolating polynomial.

applied mathematics and computation

A general recurrence relation for the weight-functions in  M\"uhlbach-Neville-Aitken representions with application to WENO  interpolation and differentiation