Quadrature Method

Quadrature methods aim to efficiently approximate integrals, a fundamental problem across numerous scientific disciplines. Current research emphasizes developing robust and versatile quadrature rules, particularly within reproducing kernel Hilbert spaces (RKHS), leveraging techniques like Bayesian quadrature and adaptive importance sampling to improve accuracy and efficiency. These advancements are driving progress in diverse fields, including Bayesian optimization, reinforcement learning, and solving partial differential equations, by enabling more precise and computationally feasible solutions to complex problems. The focus is on minimizing computational cost while maintaining accuracy, often through optimized sampling strategies and the incorporation of control variates.