JACOBI_EIGENVALUE
Eigenvalues and Eigenvectors of a Symmetric Matrix

JACOBI_EIGENVALUE, a MATLAB library 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 GNU LGPL 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:

ARPACK, a MATLAB library which uses Arnoldi methods to compute some eigenvalues and eigenvectors of matrices, which may be very large.

jacobi_eigenvalue_test

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

TEST_MAT, a MATLAB library 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.m, computes the eigenvalues and eigenvectors of a real symmetric matrix.
• r8mat_is_eigen_right.m, determines the error in a (right) eigensystem.
• r8mat_norm_fro.m, returns the Frobenius norm (square root of sum of squares) of a matrix.
• r8mat_print.m, prints an R8MAT.
• r8mat_print_some.m, prints some of an R8MAT.
• r8vec_print.m, prints an R8VEC.
• timestamp.m, prints the current YMDHMS date as a time stamp.