Iterative Solvers - Krylov Subspace Methods

• Iterative methods for

  • Ax = b and Ax = ?x

• Ingredients

  • Matrix vector multiplication Ax, possibly Atz
  • Dot products, Saxpy’s, Scaling vectors
  • “Preconditioner”, M, such that MA is better conditioned than A

• Many methods with different properties

  • For Ax = b: CG, GMRES, QMR, …
  • For Ax = ?x: Lanczos, Arnoldi, …

• Many preconditioners: Jacobi, SOR, ILU, Domain Decomposition, Multigrid, …

• Best choice problem dependent, no easy answer

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