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April 1, 2026BIT Numerical MathematicsOpen Access

Construction of optimal algorithms for function approximation in Gaussian Sobolev spaces

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This research aims to develop algorithms for function approximation in Gaussian Sobolev spaces and measure error rates.
Developed two linear approximation algorithms using n function evaluations.
First algorithm employs scaled trigonometric interpolation and works in almost-linear time.
Second algorithm utilizes spline smoothing to achieve optimal convergence rates.
The first algorithm achieves an optimal error rate of n^-α up to a logarithmic factor.
Both algorithms attain the desired convergence rate n^-α in their respective approaches.

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Implication

This analysis constructs algorithms achieving optimal convergence rates in function approximation using Gaussian Sobolev spaces, indicating effective computational methods.

Cite This Study

Suzuki et al. (2026) studied this question.

synapsesocial.com/papers/69ccb6fd16edfba7beb88cfb https://doi.org/10.1007/s10543-026-01122-y

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Implication

This analysis constructs algorithms achieving optimal convergence rates in function approximation using Gaussian Sobolev spaces, indicating effective computational methods.

Construction of optimal algorithms for function approximation in Gaussian Sobolev spaces

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Discussion

Implication

Cite This Study

Construction of optimal algorithms for function approximation in Gaussian Sobolev spaces

Key Points

Discussion

Implication

Cite This Study

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