Linear Interpolation

Linear interpolation, the process of estimating values between known data points, is a fundamental technique with applications across diverse fields. Current research focuses on improving its efficiency and accuracy in complex settings, such as optimizing neural network training (e.g., through methods like relaxed approximate proximal point algorithms) and approximating distances between probability distributions. These advancements are impacting areas ranging from image processing and generative adversarial networks to robotics and machine learning classification, where linear interpolation provides efficient and stable solutions for challenging problems. The ongoing exploration of its theoretical properties and practical applications continues to refine its role as a powerful tool in scientific computation and engineering.