POWER_METHOD
The Power Method for Eigenvalues and Eigenvectors

POWER_METHOD is a FORTRAN77 library which carries out the power method.

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 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 FORTRAN90 library which computes eigenvalues for large matrices;

EISPACK a FORTRAN77 library which carries out eigenvalue computations; superseded by LAPACK;

TEST_EIGEN, a FORTRAN77 library which implements test matrices for eigenvalue analysis.

TEST_MAT, a FORTRAN77 library which defines test matrices.

TOMS343, a FORTRAN77 library which computes the eigenvalues and eigenvectors of a general real matrix;
this is a FORTRAN77 version of ACM TOMS algorithm 343.

TOMS384, a FORTRAN77 library which computes the eigenvalues and eigenvectors of a symmetric matrix;
this is a FORTRAN77 version of ACM TOMS algorithm 384.

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.f, the source code.
• power_method.sh, commands to compile the source code.

Examples and Tests:

• power_method_prb.f, the tests;
• power_method_prb.sh, commands to compile and run the sample program.
• power_method_prb_output.txt, the output file.

List of Routines:

• FIBONACCI2 returns the FIBONACCI2 matrix.
• POWER_METHOD applies several steps of the power method.
• POWER_METHOD2 applies several steps of the power method.
• R8_EPSILON returns the R8 roundoff unit.
• R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.
• TRIS returns the TRIS matrix.
• TRIS_EIGENVALUES returns the eigenvalues of the TRIS matrix.

You can go up one level to the FORTRAN77 source codes.