Kernel Interpolation

Kernel interpolation is a technique used to estimate function values at unobserved points based on known values at scattered locations, leveraging kernel functions to define relationships between data points. Current research focuses on improving the accuracy and efficiency of kernel interpolation, particularly in high-dimensional spaces and noisy environments, exploring methods like weighted spectral filters, structured kernel interpolation (SKI), and incorporating sparse grids to address computational challenges. These advancements have significant implications for diverse fields, including sound field reconstruction, geophysical imaging, and machine learning, offering improved accuracy and scalability for various applications.