Parametric Integration by Magic Point Empirical Interpolation
Provides theoretical foundations and practical validation for a method that accelerates parametric integration across multiple scientific domains.
The paper derives analyticity criteria for error bounds and exponential convergence of the magic point empirical interpolation method, and demonstrates its effectiveness for parametric integration, particularly Fourier transforms, with numerical experiments showing exponential convergence even beyond theoretical guarantees.
We derive analyticity criteria for explicit error bounds and an exponential rate of convergence of the magic point empirical interpolation method introduced by Barrault et al. (2004). Furthermore, we investigate its application to parametric integration. We find that the method is well-suited to Fourier transforms and has a wide range of applications in such diverse fields as probability and statistics, signal and image processing, physics, chemistry and mathematical finance. To illustrate the method, we apply it to the evaluation of probability densities by parametric Fourier inversion. Our numerical experiments display convergence of exponential order, even in cases where the theoretical results do not apply.