58 citations · 216 across the 28 of their papers we have counts for
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Convex-Geometric Error Bounds for Positive-Weight Kernel Quadrature
Satoshi Hayakawa
Kernel quadrature can exploit RKHS spectral structure and outperform Monte Carlo on smooth integrands, but optimized quadrature weights are generally signed and may be numerically…
Sampling-based Nyström Approximation and Kernel Quadrature
Satoshi Hayakawa, Harald Oberhauser, Terry Lyons
We analyze the Nyström approximation of a positive definite kernel associated with a probability measure. We first prove an improved error bound for the conventional Nyström approx…
Positively Weighted Kernel Quadrature via Subsampling
Satoshi Hayakawa, Harald Oberhauser, Terry Lyons
We study kernel quadrature rules with convex weights. Our approach combines the spectral properties of the kernel with recombination results about point measures. This results in e…
Monte Carlo Cubature Construction
Satoshi Hayakawa
In numerical integration, cubature methods are effective, especially when the integrands can be well-approximated by known test functions, such as polynomials. However, the constru…
Convergence analysis of approximation formulas for analytic functions via duality for potential energy minimization
Satoshi Hayakawa, Ken'ichiro Tanaka
We investigate the approximation formulas that were proposed by Tanaka & Sugihara (2019), in weighted Hardy spaces, which are analytic function spaces with certain asymptotic decay…