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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Nonlinear quadrature formulae can be constructed for function families closed under scaling and affine transformations, achieving the same accuracy as Newton-Cotes rules with explicit error bounds.
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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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Towards non-linear quadrature formulae
Nonlinear quadrature formulae can be constructed for function families closed under scaling and affine transformations, achieving the same accuracy as Newton-Cotes rules with explicit error bounds.