diff --git a/Manifest.toml b/Manifest.toml
new file mode 100644
index 0000000..fdfb668
--- /dev/null
+++ b/Manifest.toml
@@ -0,0 +1,660 @@
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.9.3"
+manifest_format = "2.0"
+project_hash = "98aa7629eba2429fe275a54a066bb8846305026c"
+
+[[deps.AMD]]
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+weakdeps = ["StaticArrays"]
+
+    [deps.Adapt.extensions]
+    AdaptStaticArraysExt = "StaticArrays"
+
+[[deps.ArgTools]]
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+
+[[deps.ArnoldiMethod]]
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+    [deps.ArrayInterface.extensions]
+    ArrayInterfaceBandedMatricesExt = "BandedMatrices"
+    ArrayInterfaceBlockBandedMatricesExt = "BlockBandedMatrices"
+    ArrayInterfaceCUDAExt = "CUDA"
+    ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore"
+    ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore"
+    ArrayInterfaceTrackerExt = "Tracker"
+
+    [deps.ArrayInterface.weakdeps]
+    BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+    BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
+    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+    GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
+    StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+
+[[deps.Artifacts]]
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+[[deps.Base64]]
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+[[deps.BenchmarkTools]]
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+    [deps.ConstructionBase.weakdeps]
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+    ExaPFCUDAExt = "CUDA"
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+    [deps.ExaPF.weakdeps]
+    AMDGPU = "21141c5a-9bdb-4563-92ae-f87d6854732e"
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+    FiniteDiffBlockBandedMatricesExt = "BlockBandedMatrices"
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diff --git a/src/KKT/reduced_newton.jl b/src/KKT/reduced_newton.jl
index b867d1b..f7eea76 100644
--- a/src/KKT/reduced_newton.jl
+++ b/src/KKT/reduced_newton.jl
@@ -304,8 +304,8 @@ function MadNLP.compress_jacobian!(kkt::BieglerKKTSystem)
     copy_index!(nonzeros(kkt.Gu), Jv, kkt.mapGu)
     copy_index!(nonzeros(kkt.A), Jv, kkt.mapA)
 
-    # TODO: KRYLOV
-    # this is the place to update the preconditioner.
+    # Update the block-Jacobi preconditioner
+    LS.update(kkt.linear_solver.preconditioner, kkt.Gx, ExaPF.CPU())
 
     fixed!(nonzeros(kkt.Gu), kkt.ind_Gu_fixed, 0.0)
     fixed!(nonzeros(kkt.A), kkt.ind_A_fixed, 0.0)
diff --git a/src/krylov.jl b/src/krylov.jl
index 9e2fa61..3ebb1f4 100644
--- a/src/krylov.jl
+++ b/src/krylov.jl
@@ -1,13 +1,15 @@
-struct KrylovWrapper{T, SMT, K1, K2}
+struct KrylovWrapper{T, SMT, K1, K2, P}
     Gx::SMT
     solver1::K1
     solver2::K2
+    preconditioner::P
 end
 
 function KrylovWrapper{T, VT, MT}(Gx, n, p) where {T, VT, MT}
     solver1 = ExaPF.BlockGmresSolver(n, n, p, 1, VT, MT)
     solver2 = Krylov.GmresSolver(n, n, 1, VT)
-    return KrylovWrapper{T, typeof(Gx), typeof(solver1), typeof(solver2)}(Gx, solver1, solver2)
+    preconditioner = ExaPF.LS.BlockJacobiPreconditioner(Gx, 32, ExaPF.CPU())
+    return KrylovWrapper{T, typeof(Gx), typeof(solver1), typeof(solver2), typeof(preconditioner)}(Gx, solver1, solver2, preconditioner)
 end
 
 Base.size(kw::KrylovWrapper) = size(kw.Gx)
@@ -16,27 +18,27 @@ Base.size(kw::KrylovWrapper, dim::Integer) = size(kw.Gx, dim)
 LinearAlgebra.adjoint(kw::KrylovWrapper{T}) where T = LinearAlgebra.Adjoint{T, typeof(kw)}(kw)
 
 function LinearAlgebra.ldiv!(kw::KrylovWrapper{T}, x::AbstractVector{T}) where T
-    Krylov.solve!(kw.solver2, kw.Gx, x; verbose=1, atol=1e-8, rtol=0.0)
+    Krylov.solve!(kw.solver2, kw.Gx, x; N=kw.preconditioner, verbose=1, atol=1e-8, rtol=0.0)
     copyto!(x, kw.solver2.x)
     return x
 end
 
 function LinearAlgebra.ldiv!(akw::LinearAlgebra.Adjoint{T, KW}, x::AbstractVector{T}) where {T, KW<:KrylovWrapper{T}}
     kw = parent(akw)
-    Krylov.solve!(kw.solver2, kw.Gx', x; verbose=1, atol=1e-8, rtol=0.0)
+    Krylov.solve!(kw.solver2, kw.Gx', x; N=kw.preconditioner, verbose=1, atol=1e-8, rtol=0.0)
     copyto!(x, kw.solver2.x)
     return x
 end
 
 function LinearAlgebra.ldiv!(kw::KrylovWrapper{T}, X::AbstractMatrix{T}) where T
-    ExaPF.block_gmres!(kw.solver1, kw.Gx, X; verbose=1, atol=1e-10, rtol=1e-10)
+    ExaPF.block_gmres!(kw.solver1, kw.Gx, X; N=kw.preconditioner, verbose=1, atol=1e-10, rtol=1e-10)
     copyto!(X, kw.solver1.X)
     return X
 end
 
 function LinearAlgebra.ldiv!(akw::LinearAlgebra.Adjoint{T, KW}, X::AbstractMatrix{T}) where {T, KW<:KrylovWrapper{T}}
     kw = parent(akw)
-    ExaPF.block_gmres!(kw.solver1, kw.Gx', X; verbose=1, atol=1e-10, rtol=1e-10)
+    ExaPF.block_gmres!(kw.solver1, kw.Gx', X; N=kw.preconditioner, verbose=1, atol=1e-10, rtol=1e-10)
     copyto!(X, kw.solver1.X)
     return X
 end
diff --git a/test/kkt.jl b/test/kkt.jl
index 24af98b..482a829 100644
--- a/test/kkt.jl
+++ b/test/kkt.jl
@@ -80,7 +80,7 @@ function test_biegler_kkt(casename)
     return
 end
 
-@testset "BieglerKKTSystem $case" for case in ["case9.m", "case30.m", "case300.m"]
+@testset "BieglerKKTSystem $case" for case in ["case9.m", "case30.m", "case118.m", "case300.m", "case2869pegase.m", "case1354pegase.m"]
     test_biegler_kkt(case)
 end