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- W4310518171 abstract "Abstract This work is concerned with the interpolation of a function f when using a low number of interpolation points, as required by several schemes intended to solve PDEs numerically. The function f is assumed to have a jump or a steep derivative, and our goal is to minimize the oscillations produced by the Gibbs phenomenon while preserving the approximation properties for smoother functions. This is achieved by interpolating the transform ḟ ˆ = g ᴼ f using Lagrange polynomials, where g is a rational transformation chosen by minimizing a suitable functional depending on the values of f . The mapping g is monotonic and constructed to posses boundary layers that remove the Gibbs phenomenon. No previous knowledge of the location of the jump is required. The extension to functions of several variables is straightforward, of which we provide several examples. MSC Classification : 65D05 , 65D15" @default.
- W4310518171 created "2022-12-11" @default.
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- W4310518171 date "2022-12-01" @default.
- W4310518171 modified "2023-10-01" @default.
- W4310518171 title "A Lagrange-type interpolation method nearly free of oscillations" @default.
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- W4310518171 doi "https://doi.org/10.21203/rs.3.rs-2314571/v1" @default.
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