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Contents

• How to Use This Book
• Acknowledgements
• List of Figures
• Introduction
  • Why Use Templates?
  • What Methods Are Covered?
• Iterative Methods
  • Overview of the Methods
  • Stationary Iterative Methods
    • The Jacobi Method
    • The Gauss-Seidel Method
    • The Successive Overrelaxation Method
    • The Symmetric Successive Overrelaxation Method
    • Notes and References
  • Nonstationary Iterative Methods
    • Conjugate Gradient Method (CG)
    • MINRES and SYMMLQ
    • CG on the Normal Equations, CGNE and CGNR
    • Generalized Minimal Residual (GMRES)
    • BiConjugate Gradient (BiCG)
    • Quasi-Minimal Residual (QMR)
    • Conjugate Gradient Squared Method (CGS)
    • BiConjugate Gradient Stabilized (Bi-CGSTAB)
    • Chebyshev Iteration
  • Summary of the Methods
  • A short history of Krylov methods
  • Survey of recent Krylov methods
• Preconditioners
  • The why and how
    • Cost trade-off
    • Theoretical prerequisites on preconditioners
  • Jacobi Preconditioning
    • Block Jacobi Methods
    • Discussion
  • SSOR preconditioning
  • Incomplete Factorization Preconditioners
    • Creating an incomplete factorization
    • Point incomplete factorizations
    • Block factorization methods
    • Incomplete LQ factorizations
  • Polynomial preconditioners
  • Preconditioners from properties of the differential equation
    • Preconditioning by the symmetric part
    • The use of fast solvers
    • Alternating Direction Implicit methods
• Related Issues
  • Complex Systems
  • Stopping Criteria
    • More Details about Stopping Criteria
    • When or is not readily available
    • Estimating
    • Stopping when progress is no longer being made
    • Accounting for floating point errors
  • Data Structures
    • Survey of Sparse Matrix Storage Formats
    • Matrix vector products
    • Sparse Incomplete Factorizations
  • Parallelism
    • Inner products
    • Vector updates
    • Matrix-vector products
    • Preconditioning
      • Discovering parallelism in sequential preconditioners.
      • More parallel variants of sequential preconditioners.
      • Fully decoupled preconditioners.
    • Wavefronts in the Gauss-Seidel and Conjugate Gradient methods
    • Blocked operations in the GMRES method
• Remaining topics
  • The Lanczos Connection
  • Block Iterative Methods
  • Reduced System Preconditioning
  • Domain Decomposition Methods
    • Overlapping Subdomain Methods
    • Non-overlapping Subdomain Methods
    • Multiplicative Schwarz Methods
  • Multigrid Methods
  • Row Projection Methods
• Obtaining the Software
• Overview of the BLAS
• Glossary
• Notation
• References
• Index
• About this document ...