Contents

• Contents
• List of Figures
• List of Tables
• Introduction to ARPACK
  • Important Features
  • Getting Started
  • Reverse Communication Interface
  • Availability
  • Installation
  • Documentation
  • Dependence on LAPACK and BLAS
  • Expected Performance
  • P_ARPACK
  • Contributed Additions
  • Trouble Shooting and Problems
  • Research Funding of ARPACK
• Getting Started with ARPACK
  • Directory Structure and Contents
  • Getting Started
  • An Example for a Symmetric Eigenvalue Problem
    • The Reverse Communication Interface
    • Post Processing for Eigenvalues and Eigenvectors
    • Setting up the problem
    • Storage Declarations
    • Stopping Criterion
    • Initial Parameter Settings
    • Setting the Starting Vector
    • Trace Debugging Capability
• General Use of ARPACK
  • Naming Conventions, Precisions and Types
  • Shift and Invert Spectral Transformation Mode
    • ${\bf M}$ is Hermitian Positive Definite
    • ${\bf M}$ is NOT Hermitian Positive Semi-Definite
  • Reverse Communication Structure for Shift-Invert
    • Shift and invert on a Generalized Eigen-problem
  • Using the Computational Modes
  • Computational Modes for Real Symmetric Problems
  • Post-Processing for Eigenvectors Using dseupd
  • Computational Modes for Real Non-Symmetric Problems
  • Post-Processing for Eigenvectors Using dneupd
  • Computational Modes for Complex Problems
  • Post-Processing for Eigenvectors Using zneupd
• The Implicitly Restarted Arnoldi Method
  • Structure of the Eigenvalue Problem
  • Krylov Subspaces and Projection Methods
  • The Arnoldi Factorization
  • Restarting the Arnoldi Method
    • Implicit Restarting
    • Block Methods
  • The Generalized Eigenvalue Problem
    • Structure of the Spectral Transformation
    • Eigenvector/Null-Space Purification
  • Stopping Criterion
• Computational Routines
  • ARPACK subroutines
    • XYaupd
    • XYaup2
    • XYaitr
    • Xgetv0
    • Xneigh
    • [s,d]seigt
    • [s,d]Yconv
    • XYapps
    • XYeupd
  • LAPACK routines used by ARPACK
  • BLAS routines used by ARPACK
• Templates and Driver Routines
  • Symmetric Drivers
    • Selecting a Symmetric Driver
      • Standard Mode
      • Shift-Invert Mode
      • Generalized Eigenvalue Problem
      • Regular Inverse Mode
      • Shift-Invert Mode
      • Buckling Mode
      • Cayley Transformation Mode
    • Identify OP and B for the Driver
    • The Reverse Communication Interface
      • Driver dsdrv1
      • Driver dsdrv2
      • Driver dsdrv3
      • Driver dsdrv4
      • Driver dsdrv5
      • Driver dsdrv6
    • Modify the Problem Dependent Variables
      • Other Variables
    • Postprocessing and Accuracy Checking
  • Real Nonsymmetric Drivers
    • Selecting a Non-symmetric Driver
      • Standard Mode
      • Shift-Invert Mode
      • Generalized Nonsymmetric Eigenvalue Problem
      • Regular Inverse Mode
      • Spectral Transformations for Non-symmetric Eigenvalue Problems
    • Identify OP and B for the Driver
    • The Reverse Communication Interface
      • Driver dndrv1
      • Driver dndrv2
      • Driver dndrv3
      • Driver dndrv4
      • Driver dndrv5
      • Driver dndrv6
    • Modify the Problem Dependent Variables
      • Other Variables
    • Postprocessing and Accuracy Checking
  • Complex Drivers
    • Selecting a Complex Arithmetic Driver
      • Standard Mode
      • Shift and Invert Spectral Transformation
      • Generalized Eigenvalue Problems
      • Regular Inverse Mode
      • General Shift-Invert Spectral Transformation
    • Identify OP and B for the Driver to be Modified
    • The Reverse Communication Interface
      • Driver zndrv1
      • Driver zndrv2
      • Driver zndrv3
      • Driver zndrv4
    • Modify the Problem Dependent Variables
      • Other Variables
    • Post-processing and Accuracy Checking
  • Band Drivers
    • Selecting a Band Storage Driver
    • Store the matrix correctly
    • Modify problem dependent variables
    • Modify other variables if necessary
    • Accuracy checking
  • The Singular Value Decomposition
    • The SVD Drivers
• Tracking the progress of ARPACK
  • Obtaining Trace Output
  • Check Pointing ARPACK
• The XYaupd ARPACK Routines
  • DSAUPD
  • DNAUPD
  • ZNAUPD
• References
• Index