High-Order Approximation of Set-Valued Functions

Nira Dyn, Elza Farkhi, Alona Mokhov

Research output: Contribution to journalArticlepeer-review


We introduce the notion of metric divided differences of set-valued functions. With this notion we obtain bounds on the error in set-valued metric polynomial interpolation. These error bounds lead to high-order approximations of set-valued functions by metric piecewise-polynomial interpolants of high degree. Moreover, we derive high-order approximation of set-valued functions by local metric approximation operators reproducing high-degree polynomials.

Original languageEnglish
JournalConstructive Approximation
StateAccepted/In press - 2022


  • High-order approximation
  • Metric linear combinations
  • Metric local linear operators
  • Set-valued functions
  • Set-valued metric divided differences
  • Set-valued metric polynomial interpolation


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