Quasi-interpolation for near-boundary approximations

Anat Amir, David Levin

Research output: Contribution to journalArticlepeer-review


In this work we address the problem of approximating a smooth function on a bounded domain from a set of data points on which we know the values of the objective function. While we can generally guarantee impressive approximations in the interior of the domain, the theory does not extend to the boundary of the do¬main. Indeed, numerical experiments present all forms of artifacts when performing approximations near the boundary of the domain. To achieve adequate approxi¬mations near boundaries, we will build upon our previous work, in which we have managed to construct high-order approximations to singular functions. By consid¬ering the boundary of the domain as a singularity, we show that we can similarly return high-order approximations to the objective function, even in the immediate vicinity of the boundary of the domain.

Original languageEnglish
Pages (from-to)67-89
Number of pages23
JournalJaen Journal on Approximation
Issue number1-2
StatePublished - 1 Dec 2019


  • Moving least squares
  • Multivariate functions
  • Quasi-interpolation


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