Inverse Power Method

This method is used to find the smallest Eigen value in modulus of the given matrix by employing power method to the inverse matrix A^(-1).

If the given matrix A is non – singular then the Eigen values of A −1 are just the reciprocal of the Eigen values of A and conversely.

Thus if λ not equal to 0 is an Eigen value of a matrix A then 1/λ is the Eigen Value of the matrix A^(−1) . The dominant Eigen value of the matrix A^(−1) is the smallest Eigen value of A, thus the inverse power method is used to find the smallest Eigen value in modulus of the given matrix by employing power method to the inverse matrix A^(−1).