List of Figures

• An example of the reverse communication interface used by ARPACK.
• The ARPACK directory structure.
• The reverse communication interface in example program dssimp.
• Post Processing for Eigenvalues and Eigenvectors using desupd.
• Storage declarations needed for ARPACK subroutine dsaupd
• How to initiate the trace debugging capability in ARPACK.
• Output from a Debug session for dsaupd.
• Reverse communication interface for Shift-Invert.
• Reverse communication interface for Shift-Invert contd.
• Calling the ARPACK subroutine dnaupd.
• Calling the ARPACK subroutine dsaupd.
• Post-Processing for Eigenvectors Using dseupd.
• Calling sequence of subroutine dnaupd.
• Post-Processing for Eigenvectors Using dneupd.
• Calling the ARPACK subroutine znaupd.
• Post-Processing for Eigenvectors Using cneupd.
• The Implicitly Restarted Arnoldi Method in ARPACK.
• Algorithm 1: Shifted QR-iteration.
• Algorithm 2: The k-Step Arnoldi Factorization
• Algorithm 3: An Implicitly Restarted Arnoldi Method (IRAM).
• After performing m-k implicitly shifted QR steps on , the middle set of pictures illustrates The last p columns of are nonzero because of the QR iteration.

• Total filter polynomial from an IRA iteration.
• Total Filter Polynomial with Spectral Transformation
•  XYaupd - Implementation of the IRAM/IRLM in ARPACK
• Outline of algorithm used by subroutine XYeupd to compute Schur vectors and possibly eigenvectors.
• Reverse communication structure
• Compute by Blocks
• Sample output produced by dsaupd.
• The include file debug.h.
• Reading in a previous state with the example program dssave.
• Writing a state with the example program dssave.
• Writing a state with the example program dssave contd.