Numerical Analysis Questions
The power method is a numerical algorithm used in numerical analysis to find the dominant eigenvalue and corresponding eigenvector of a matrix. It is an iterative method that starts with an initial guess for the eigenvector and repeatedly multiplies the matrix by the current eigenvector approximation, normalizing it at each iteration. As the iterations progress, the eigenvector approximation converges to the dominant eigenvector, and the corresponding eigenvalue can be obtained by taking the dot product of the matrix multiplied by the eigenvector approximation with the eigenvector approximation itself. The power method is particularly useful for large matrices and can be used to solve a variety of problems, such as finding the principal component of a dataset or determining the steady-state behavior of a Markov chain.