The power method is an iterative method used to find the largest in magnitude eigenvalue of a linear system and it's corresponding eigenvector. Each iterative step takes O(N²) time.

The Jacobi method is an iterative method that can be used to find all eigenvalues and corresponding eigenvectors of a Hermitian matrix. It is based on the fact that orthogonal transformations on such a matrix do not change its eigenvalues, and hence these transformations can be iteratvely made in order to transform the matrix into a diagonal matrix in which the diagonal entries are the eigenvalues. The run time of a single iteration is O(N²).

There are two main programs in this project, eigen.py and tests.py. The former program contains the code for each iterative method listed above, and the latter contains the code to run the methods in the test cases found in the data directory, and visualizes the iterations. eigen.py can also be run on an individual matrix read from standard input.

• eigen.py:

  python3 eigen.py [-h] [--jacobi]
  

  • -h => print usage information
  • –jacobi => use the Jacobi method (power method is the default)

• tests.py:

  python3 tests.py [-t <threshold>] [-g] [-h] [-e] <test-number>
  

  • -h => print usage information
  • -t => the threshold for convergence of both algorithms (default 0.0001)
  • -g => generate a new test case and print to stdout
  • -e => print the test case in latex format
  • test-number => the number of the test case in the data directory