The Power method is an ______ used to determine the dominant eigenvalue of a matrix

The Power method is an iterative algorithm used to determine the dominant eigenvalue of a matrix. This technique is particularly useful for large matrices, where direct methods may be computationally expensive or infeasible. The key idea is to start with an initial vector and repeatedly multiply it by the matrix, normalizing the result at each step. As the process continues, the vector converges to the eigenvector associated with the dominant eigenvalue, while the ratio of successive iterations gives an approximation of that eigenvalue.

This method is widely applied in various fields, including economics, engineering, and data science, particularly in applications involving Markov chains and Google's PageRank algorithm. The simplicity of the Power method makes it a popular choice for estimating eigenvalues in practical scenarios, although it might require several iterations to reach the desired level of accuracy.