ABSTRACT
This chapter presents numerical methods to approximate the eigenvalues and eigenvectors of a matrix. The power method is an iterative method that estimates the dominant eigenvalue of a matrix and its corresponding eigenvector. Once the largest or smallest eigenvalue of a matrix is known, the remaining eigenvalues can be approximated using the shifted inverse power method. The user-defined function ShiftInvPower uses the shifted inverse power method to estimate the eigenvalue of a square matrix closest to a specified value. It also returns the eigenvector associated with the desired eigenvalue. The user-defined function Householder QR uses Householder's method to transform a real, symmetric matrix into a tridiagonal matrix, to which the QR factorization is repeatedly applied in order to obtain a tridiagonal matrix whose diagonal entries are much larger in magnitude than those along the upper- and lower-diagonals. The built-in function in MATLAB finds the eigenvalues and eigenvectors of a matrix.
