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math.NA2025

Lattice Rules Meet Kernel Cubature

Vesa Kaarnioja, Ilja Klebanov, Claudia Schillings +1

Rank-1 lattice rules are a class of equally weighted quasi-Monte Carlo methods that achieve essentially linear convergence rates for functions in a reproducing kernel Hilbert space…

math.NA2024

Möbius-Transformed Trapezoidal Rule

Yuya Suzuki, Nuutti Hyvönen, Toni Karvonen

We study numerical integration by combining the trapezoidal rule with a Möbius transformation that maps the unit circle onto the real line. We prove that the resulting transformed…

math.NA2024

Construction of Optimal Algorithms for Function Approximation in Gaussian Sobolev Spaces

Yuya Suzuki, Toni Karvonen

This paper studies function approximation in Gaussian Sobolev spaces over the real line and measures the error in a Gaussian-weighted -norm. We construct two linear approximat…