power_method

power_method, a C code which carries out the power method, which seeks the dominant eigenvalue and corresponding eigenvector of a matrix.

The power method seeks to determine the eigenvalue of maximum modulus, and a corresponding eigenvector.

The 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.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

power_method is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

power_method_test

test_eigen, a C code which implements test matrices for eigenvalue analysis.

test_matrix, a C code which defines 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.
3. Gene Golub, Charles VanLoan,
   Matrix Computations, Third Edition,
   Johns Hopkins, 1996,
   ISBN: 0-8018-4513-X,
   LC: QA188.G65.

Source Code:

• power_method.c, the source code.
• power_method.sh, compiles the source code.
• power_method.h, the include file.