SPIDeC methods achieve arbitrarily high-order accuracy for positive dynamical systems while unconditionally preserving positivity and equilibria via a multiplicative Volterra structure, and they are L-stable with asymptotic logarithmic contractivity under Gauss-Radau nodes.
Barycentric Lagrange Interpolation
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If angular perturbations satisfy n σ_n (log n +1) bounded by a small constant, perturbed Chebyshev-Lobatto nodes retain logarithmic Lebesgue constants, with an obstruction at angular scale 1/n.
Dynamic Time Warping with a shared warping path across parameters aligns binary stellar tracks for accurate interpolation while preserving physical relationships such as the Stefan-Boltzmann law.
DMK extended to rectangular cuboids with arbitrary periodicity via localized octree evaluations on cubical tilings and Fourier-space root-level summation with truncated kernels for reduced periodicity.
Finite post-peak detector-frame windows for GW250114 yield a stable common-remnant Kerr interpretation after calibration on synthetic waveforms and robustness checks.
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Stable Positive Integral Deferred Correction Methods for Positive Dynamical Systems
SPIDeC methods achieve arbitrarily high-order accuracy for positive dynamical systems while unconditionally preserving positivity and equilibria via a multiplicative Volterra structure, and they are L-stable with asymptotic logarithmic contractivity under Gauss-Radau nodes.
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When do perturbed Chebyshev--Lobatto points remain Chebyshev?
If angular perturbations satisfy n σ_n (log n +1) bounded by a small constant, perturbed Chebyshev-Lobatto nodes retain logarithmic Lebesgue constants, with an obstruction at angular scale 1/n.
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Irregularly Sampled Time Series Interpolation for Binary Evolution Simulations Using Dynamic Time Warping
Dynamic Time Warping with a shared warping path across parameters aligns binary stellar tracks for accurate interpolation while preserving physical relationships such as the Stefan-Boltzmann law.
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Fast summation on rectangular cuboids with arbitrary periodicity in the DMK framework
DMK extended to rectangular cuboids with arbitrary periodicity via localized octree evaluations on cubical tilings and Fourier-space root-level summation with truncated kernels for reduced periodicity.
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Deterministic Trust Regions for Finite-Window Black-Hole Spectroscopy in GW250114
Finite post-peak detector-frame windows for GW250114 yield a stable common-remnant Kerr interpretation after calibration on synthetic waveforms and robustness checks.