Power Method

The power method is an iterative algorithm used to find the dominant eigenvector and eigenvalue of a matrix, crucial for various applications in data analysis and scientific computing. Current research focuses on extending the power method's capabilities, including developing variants for specific matrix types (e.g., dual quaternion Hermitian matrices) and integrating it into other algorithms like streaming PCA and gradient descent methods to improve efficiency and address fairness concerns. These advancements enhance the power method's utility in diverse fields, from machine learning (e.g., community detection) and signal processing to solving large-scale linear eigenvalue problems and improving the accuracy of parallel numerical computations.