Preconditioners

Examples

A = sprand(1000, 1000, 0.01)
A = A + A' + 30I

# Diagonal preconditioner
p = DiagonalPreconditioner(A)

# Incomplete Cholesky preconditioner with cut-off level 2
p = CholeskyPreconditioner(A, 2)

# Algebraic multigrid preconditioner (AMG)
# Ruge-Stuben variant
p = AMGPreconditioner{RugeStuben}(A)
# Smoothed aggregation
p = AMGPreconditioner{SmoothedAggregation}(A)

# Solve the system of equations
b = A*ones(1000)
x = cg(A, b, Pl=p)

A = sprand(1000, 1000, 0.01)
A = A + A' + 30I
# Updates the preconditioner with the new matrix A
UpdatePreconditioner!(p, A)

Advanced AMG preconditioners

More advanced AMG preconditioners are also possible by building the MultiLevel struct that AMGPreconditioner wraps yourself using the package AMG.jl.

Citing Preconditioners.jl

If you use Preconditioners for your own research, please consider citing the following publication: Mohamed Tarek. Preconditioners.jl: A Flexible and Extensible Framework for Preconditioning in Iterative Solvers. 2023. doi: 10.13140/RG.2.2.26655.02721.

@article{MohamedTarekPreconditionersjl,
  doi = {10.13140/RG.2.2.26655.02721},
  url = {https://rgdoi.net/10.13140/RG.2.2.26655.02721},
  author = {Tarek,  Mohamed},
  language = {en},
  title = {Preconditioners.jl: A Flexible and Extensible Framework for Preconditioning in Iterative Solvers},
  year = {2023}
}