POWER_METHOD
The Power Method for Eigenvalues and Eigenvectors

POWER_METHOD is a MATLAB library which carries out the power method.

The power method implemented here is given a real square matrix, and seeks to determine the eigenvalue of maximum modulus, and a corresponding eigenvector.

The basic power method will not perform as expected if, corresponding to the maximum modulus, there are complex eigenvalues, or a pair of real eigenvalues of opposite sign. The power method's behavior can break down or be very slow initially if the starting vector has a zero or very small component in the eigenspace corresponding to the maximal eigenvalue.

A second version of the power method is included which can handle the case of complex eigenvalues.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

POWER_METHOD is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

ARPACK, a MATLAB library which computes eigenvalues and eigenvectors of large sparse matrices, accessible via the built-in EIGS command;

TEST_MAT, a MATLAB library which defines test matrices.

TEST_MATRIX, a MATLAB library which contains Nick Higham's collection of test matrices.

Reference:

1. Richard Burden, Douglas Faires,
   Numerical Analysis,
   Thomson Brooks/Cole, 2004,
   ISBN13: 978-0534392000,
   LC: QA297.B84.
2. Ward Cheney, David Kincaid,
   Numerical Mathematics and Computing,
   Brooks-Cole Publishing, 2004,
   ISBN: 0534201121,
   LC: QA297.C426.
3. Gene Golub, Charles VanLoan,
   Matrix Computations, Third Edition,
   Johns Hopkins, 1996,
   ISBN: 0-8018-4513-X,
   LC: QA188.G65.
4. Eric VanDeVelde,
   Concurrent Scientific Programming,
   Springer, 1994,
   ISBN: 0-387-94195-9,
   LC: QA76.58.V35.

Source Code:

• power_method.m, applies the power method seeking a real eigenvalue.
• power_method2.m, applies the power method seeking a possibly complex eigenvalue.

Examples and Tests:

• power_method_test.m, the tests;
• power_method_test_output.txt, the output file.

You can go up one level to the MATLAB source codes.