3 papers
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…
stat.ME2024
Probabilistic Richardson Extrapolation
Chris. J. Oates, Toni Karvonen, Aretha L. Teckentrup +2
For over a century, extrapolation methods have provided a powerful tool to improve the convergence order of a numerical method. However, these tools are not well-suited to modern c…