Adaptive interpolation with maximum order close to discontinuities

Francesc Aràndiga and Dionisio F. Yáñez

Applied Mathematics and Computation, 2022, vol. 418, issue C

Abstract: Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids the Gibbs phenomenon when we approximate a discontinuous function. In this work, we present a generalization to this method giving explicit expressions for all the weights for any order of the algorithm. It has a similar behavior to weighted essentially non oscillatory (WENO) technique but the design of the weights in this case is more simple. Also, we propose a new way to construct them obtaining the maximum order near the discontinuities. Some experiments are performed to demonstrate our results and to compare them with standard methods.

Keywords: Rational interpolation; Order; Point-value interpolation; Optimal weights; WENO schemes (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321008778

DOI: 10.1016/j.amc.2021.126795

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