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SABER: Stable adaptive barycentric extension for reconstruction of high-dimensional functions
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DOI：10.1016/j.cnsns.2026.110486.png)
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Abstract
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• Novel framework: introduced the sparse adaptive barycentric extension for reconstruction (saber) framework for efficient high-dimensional function approximation. • Theoretical rigor: derived backward-error-type estimates for tensor-product barycentric formulations, demonstrating linear error growth with respect to dimension and grid size. • Adaptive refinement: developed a greedy node insertion strategy based on Leja-type potentials to moderate the Lebesgue constant and enhance numerical stability in high-dimensional settings. • Shock handling: integrated shock-driven domain decomposition with localized low-order coupling, effectively mitigating Gibbs oscillations in discontinuous problems. • Numerical validation: demonstrated superior performance in reducing oscillations and maintaining approximation accuracy across challenging, highly oscillatory, and anisotropic test functions.
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