jacobi_eigenvalue

jacobi_eigenvalue, a Python code which computes the eigenvalues and eigenvectors of a real symmetric matrix.

Given a real symmetric NxN matrix A, JACOBI_EIGENVALUE carries out an iterative procedure known as Jacobi's iteration, to determine a N-vector D of real, positive eigenvalues, and an NxN matrix V whose columns are the corresponding eigenvectors, so that, for each column J of the eigenmatrix:

        A * Vj = Dj * Vj
      

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

jacobi_eigenvalue is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

test_mat, a Python code which defines test matrices, some of which have known determinants, eigenvalues and eigenvectors, inverses and so on.

Reference:

1. Gene Golub, Charles VanLoan,
   Matrix Computations, Third Edition,
   Johns Hopkins, 1996,
   ISBN: 0-8018-4513-X,
   LC: QA188.G65.

Source Code:

• jacobi_eigenvalue.py, the source code.
• jacobi_eigenvalue.sh, runs all the tests.
• jacobi_eigenvalue.txt, the output file.