The Jacobi-Davidson method for eigenproblems

The Jacobi-Davidson method is an iterative subspace method for computing one or more eigenvalues and eigenvectors of an eigenproblem. The Jacobi-Davidson (JD) method has been developed by Gerard Sleijpen and Henk van der Vorst. Publications on Jacobi-Davidson methods can be found on their home pages.

The JD Gateway provides interesting background information on Jacobi-Davidson, references, links to software, and so on.

The JDQR and JDQZ method, by Diederik Fokkema, Gerard Sleijpen and Henk van der Vorst, are based on the JD method. In these methods an effective restart strategy is incorporated. JDQR computes solutions of the standard eigenproblem and JDQZ computes solutions of the generalized eigenproblem. Currently two Jacobi-Davidson packages are available.

Jacobi-Davidson packages

• Matlab® 5.1 implementation of JDQR and JDQZ
  These codes can be found on the JDQR and the JDQZ page of Gerard Sleijpen.
  (The MATLAB JDQZ page is under construction).
• Fortran 77 implementation of JDQZ
  In Fortran 77 only the JDQZ algorithm for the generalized eigenproblem is available. However, with B=I, JDQZ can also solve the standard eigenproblem, of course. More information about the package can be found in the manual by Diederik Fokkema and Martin van Gijzen.

Obtaining the code

Note that the Fortran code is provided on an "as is" basis. The authors provide no warranty whatsoever, either expressed or implied, regarding the work, including warranties with respect to its merchantability or fitness for any particular purpose. Moreover, note that permission to copy all or part of this code is granted, provided that the copies are not made or distributed for resale: The code is distributed under the terms of the GNU General Public License (version 3 of the License, or any later version) as published by the Free Software Foundation.