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