Hankel Matrix

Hankel matrices, characterized by constant skew-diagonals, are finding increasing application in diverse fields due to their ability to represent structured data efficiently. Current research focuses on leveraging Hankel structure for faster computations, particularly in Gaussian process inference and system identification, often employing algorithms like structured Newton-like descent to address ill-conditioned matrices and improve robustness to noise. These advancements are improving the efficiency and accuracy of various applications, including signal processing, machine learning (e.g., recommendation systems and image inpainting), and control systems, by enabling more efficient algorithms and better handling of noisy or incomplete data. The development of novel algorithms and theoretical analyses continues to refine the understanding and application of Hankel matrices in these areas.