Power Iteration

Power iteration is an iterative algorithm used to find the dominant eigenvector of a matrix or tensor, with applications spanning diverse fields like graph analysis and machine learning. Current research focuses on refining its application in tensor decomposition and addressing challenges like over-smoothing in graph convolutional networks, where power iteration is shown to be a fundamental underlying process. Improved theoretical understanding of convergence rates and the development of robust variants, such as those incorporating semidefinite programming, are key areas of investigation, impacting the accuracy and efficiency of various data analysis techniques. These advancements have implications for problems like tensor principal component analysis and directed acyclic graph learning, leading to improved algorithms for data analysis and model inference.