diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 173e340d4..ef6bd5dae 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -17,6 +17,8 @@ jobs:
         version:
           - '1'
           - '1.6'
+          - '1.7'
+          - '1.8'
         include:
           - version: '1'
             group: 'LinearSolveHYPRE'
diff --git a/src/LinearSolve.jl b/src/LinearSolve.jl
index ee4a10acb..039144fbd 100644
--- a/src/LinearSolve.jl
+++ b/src/LinearSolve.jl
@@ -153,12 +153,14 @@ end
     end
 end
 
-PrecompileTools.@compile_workload begin
-    A = sprand(4, 4, 0.3) + I
-    b = rand(4)
-    prob = LinearProblem(A, b)
-    sol = solve(prob) # in case sparspak is used as default
-    sol = solve(prob, SparspakFactorization())
+@static if VERSION > v"1.9-"
+    PrecompileTools.@compile_workload begin
+        A = sprand(4, 4, 0.3) + I
+        b = rand(4)
+        prob = LinearProblem(A * A', b)
+        sol = solve(prob) # in case sparspak is used as default
+        sol = solve(prob, SparspakFactorization())
+    end
 end
 
 export LUFactorization, SVDFactorization, QRFactorization, GenericFactorization,
diff --git a/src/factorization.jl b/src/factorization.jl
index e6feb6121..53f0ec770 100644
--- a/src/factorization.jl
+++ b/src/factorization.jl
@@ -120,7 +120,7 @@ function init_cacheval(alg::Union{LUFactorization, GenericLUFactorization},
     nothing
 end
 
-@static if VERSION < v"1.7-"
+@static if VERSION < v"1.9-"
     function init_cacheval(alg::Union{LUFactorization, GenericLUFactorization},
         A::Union{Diagonal, SymTridiagonal}, b, u, Pl, Pr,
         maxiters::Int, abstol, reltol, verbose::Bool,
@@ -188,7 +188,7 @@ function init_cacheval(alg::QRFactorization, A::AbstractSciMLOperator, b, u, Pl,
     nothing
 end
 
-@static if VERSION < v"1.7-"
+@static if VERSION < v"1.9-"
     function init_cacheval(alg::QRFactorization,
         A::Union{Diagonal, SymTridiagonal, Tridiagonal}, b, u, Pl, Pr,
         maxiters::Int, abstol, reltol, verbose::Bool,
@@ -220,7 +220,7 @@ end
 
 function CholeskyFactorization(; pivot = nothing, tol = 0.0, shift = 0.0, perm = nothing)
     if pivot === nothing
-        pivot = @static if VERSION < v"1.7beta"
+        pivot = @static if VERSION < v"1.8beta"
             Val(false)
         else
             NoPivot()
@@ -229,16 +229,30 @@ function CholeskyFactorization(; pivot = nothing, tol = 0.0, shift = 0.0, perm =
     CholeskyFactorization(pivot, 16, shift, perm)
 end
 
-function do_factorization(alg::CholeskyFactorization, A, b, u)
-    A = convert(AbstractMatrix, A)
-    if A isa SparseMatrixCSC
-        fact = cholesky!(A; shift = alg.shift, check = false, perm = alg.perm)
-    elseif alg.pivot === Val(false) || alg.pivot === NoPivot()
-        fact = cholesky!(A, alg.pivot; check = false)
-    else
-        fact = cholesky!(A, alg.pivot; tol = alg.tol, check = false)
+@static if VERSION > v"1.8-"
+    function do_factorization(alg::CholeskyFactorization, A, b, u)
+        A = convert(AbstractMatrix, A)
+        if A isa SparseMatrixCSC
+            fact = cholesky!(A; shift = alg.shift, check = false, perm = alg.perm)
+        elseif alg.pivot === Val(false) || alg.pivot === NoPivot()
+            fact = cholesky!(A, alg.pivot; check = false)
+        else
+            fact = cholesky!(A, alg.pivot; tol = alg.tol, check = false)
+        end
+        return fact
+    end
+else
+    function do_factorization(alg::CholeskyFactorization, A, b, u)
+        A = convert(AbstractMatrix, A)
+        if A isa SparseMatrixCSC
+            fact = cholesky!(A; shift = alg.shift, perm = alg.perm)
+        elseif alg.pivot === Val(false) || alg.pivot === NoPivot()
+            fact = cholesky!(A, alg.pivot)
+        else
+            fact = cholesky!(A, alg.pivot; tol = alg.tol)
+        end
+        return fact
     end
-    return fact
 end
 
 function init_cacheval(alg::CholeskyFactorization, A, b, u, Pl, Pr,
@@ -247,7 +261,7 @@ function init_cacheval(alg::CholeskyFactorization, A, b, u, Pl, Pr,
     ArrayInterface.cholesky_instance(convert(AbstractMatrix, A), alg.pivot)
 end
 
-@static if VERSION < v"1.7beta"
+@static if VERSION < v"1.8beta"
     cholpivot = Val(false)
 else
     cholpivot = NoPivot()
@@ -268,7 +282,7 @@ function init_cacheval(alg::CholeskyFactorization,
     nothing
 end
 
-@static if VERSION < v"1.7beta"
+@static if VERSION < v"1.9beta"
     function init_cacheval(alg::CholeskyFactorization,
         A::Union{SymTridiagonal, Tridiagonal}, b, u, Pl, Pr,
         maxiters::Int, abstol, reltol, verbose::Bool,
@@ -361,7 +375,7 @@ function init_cacheval(alg::SVDFactorization, A, b, u, Pl, Pr,
     nothing
 end
 
-@static if VERSION < v"1.7-"
+@static if VERSION < v"1.9-"
     function init_cacheval(alg::SVDFactorization,
         A::Union{Diagonal, SymTridiagonal, Tridiagonal}, b, u, Pl, Pr,
         maxiters::Int, abstol, reltol, verbose::Bool,
@@ -852,22 +866,42 @@ function init_cacheval(alg::CHOLMODFactorization,
     PREALLOCATED_CHOLMOD
 end
 
-function SciMLBase.solve!(cache::LinearCache, alg::CHOLMODFactorization; kwargs...)
-    A = cache.A
-    A = convert(AbstractMatrix, A)
+@static if VERSION > v"1.8-"
+    function SciMLBase.solve!(cache::LinearCache, alg::CHOLMODFactorization; kwargs...)
+        A = cache.A
+        A = convert(AbstractMatrix, A)
 
-    if cache.isfresh
-        cacheval = @get_cacheval(cache, :CHOLMODFactorization)
-        fact = cholesky(A; check = false)
-        if !LinearAlgebra.issuccess(fact)
-            ldlt!(fact, A; check = false)
+        if cache.isfresh
+            cacheval = @get_cacheval(cache, :CHOLMODFactorization)
+            fact = cholesky(A; check = false)
+            if !LinearAlgebra.issuccess(fact)
+                ldlt!(fact, A; check = false)
+            end
+            cache.cacheval = fact
+            cache.isfresh = false
         end
-        cache.cacheval = fact
-        cache.isfresh = false
+
+        cache.u .= @get_cacheval(cache, :CHOLMODFactorization) \ cache.b
+        SciMLBase.build_linear_solution(alg, cache.u, nothing, cache)
     end
+else
+    function SciMLBase.solve!(cache::LinearCache, alg::CHOLMODFactorization; kwargs...)
+        A = cache.A
+        A = convert(AbstractMatrix, A)
+
+        if cache.isfresh
+            cacheval = @get_cacheval(cache, :CHOLMODFactorization)
+            fact = cholesky(A)
+            if !LinearAlgebra.issuccess(fact)
+                ldlt!(fact, A)
+            end
+            cache.cacheval = fact
+            cache.isfresh = false
+        end
 
-    cache.u .= @get_cacheval(cache, :CHOLMODFactorization) \ cache.b
-    SciMLBase.build_linear_solution(alg, cache.u, nothing, cache)
+        cache.u .= @get_cacheval(cache, :CHOLMODFactorization) \ cache.b
+        SciMLBase.build_linear_solution(alg, cache.u, nothing, cache)
+    end
 end
 
 ## RFLUFactorization
@@ -909,7 +943,7 @@ function init_cacheval(alg::RFLUFactorization,
     nothing, nothing
 end
 
-@static if VERSION < v"1.7-"
+@static if VERSION < v"1.9-"
     function init_cacheval(alg::RFLUFactorization,
         A::Union{Diagonal, SymTridiagonal, Tridiagonal}, b, u, Pl, Pr,
         maxiters::Int,
@@ -954,7 +988,7 @@ end
 
 function NormalCholeskyFactorization(; pivot = nothing)
     if pivot === nothing
-        pivot = @static if VERSION < v"1.7beta"
+        pivot = @static if VERSION < v"1.8beta"
             Val(false)
         else
             NoPivot()
@@ -966,7 +1000,7 @@ end
 default_alias_A(::NormalCholeskyFactorization, ::Any, ::Any) = true
 default_alias_b(::NormalCholeskyFactorization, ::Any, ::Any) = true
 
-@static if VERSION < v"1.7beta"
+@static if VERSION < v"1.8beta"
     normcholpivot = Val(false)
 else
     normcholpivot = NoPivot()
@@ -996,7 +1030,7 @@ function init_cacheval(alg::NormalCholeskyFactorization,
     nothing
 end
 
-@static if VERSION < v"1.7-"
+@static if VERSION < v"1.9-"
     function init_cacheval(alg::NormalCholeskyFactorization,
         A::Union{Tridiagonal, SymTridiagonal, Adjoint}, b, u, Pl, Pr,
         maxiters::Int, abstol, reltol, verbose::Bool,
@@ -1005,26 +1039,54 @@ end
     end
 end
 
-function SciMLBase.solve!(cache::LinearCache, alg::NormalCholeskyFactorization;
-    kwargs...)
-    A = cache.A
-    A = convert(AbstractMatrix, A)
-    if cache.isfresh
+@static if VERSION > v"1.8-"
+    function SciMLBase.solve!(cache::LinearCache, alg::NormalCholeskyFactorization;
+        kwargs...)
+        A = cache.A
+        A = convert(AbstractMatrix, A)
+        if cache.isfresh
+            if A isa SparseMatrixCSC
+                fact = cholesky(Symmetric((A)' * A, :L); check = false)
+            else
+                fact = cholesky(Symmetric((A)' * A, :L), alg.pivot; check = false)
+            end
+            cache.cacheval = fact
+            cache.isfresh = false
+        end
         if A isa SparseMatrixCSC
-            fact = cholesky(Symmetric((A)' * A, :L))
+            cache.u .= @get_cacheval(cache, :NormalCholeskyFactorization) \ (A' * cache.b)
+            y = cache.u
         else
-            fact = cholesky(Symmetric((A)' * A, :L), alg.pivot)
+            y = ldiv!(cache.u,
+                @get_cacheval(cache, :NormalCholeskyFactorization),
+                A' * cache.b)
         end
-        cache.cacheval = fact
-        cache.isfresh = false
+        SciMLBase.build_linear_solution(alg, y, nothing, cache)
     end
-    if A isa SparseMatrixCSC
-        cache.u .= @get_cacheval(cache, :NormalCholeskyFactorization) \ (A' * cache.b)
-        y = cache.u
-    else
-        y = ldiv!(cache.u, @get_cacheval(cache, :NormalCholeskyFactorization), A' * cache.b)
+else
+    function SciMLBase.solve!(cache::LinearCache, alg::NormalCholeskyFactorization;
+        kwargs...)
+        A = cache.A
+        A = convert(AbstractMatrix, A)
+        if cache.isfresh
+            if A isa SparseMatrixCSC
+                fact = cholesky(Symmetric((A)' * A, :L))
+            else
+                fact = cholesky(Symmetric((A)' * A, :L), alg.pivot)
+            end
+            cache.cacheval = fact
+            cache.isfresh = false
+        end
+        if A isa SparseMatrixCSC
+            cache.u .= @get_cacheval(cache, :NormalCholeskyFactorization) \ (A' * cache.b)
+            y = cache.u
+        else
+            y = ldiv!(cache.u,
+                @get_cacheval(cache, :NormalCholeskyFactorization),
+                A' * cache.b)
+        end
+        SciMLBase.build_linear_solution(alg, y, nothing, cache)
     end
-    SciMLBase.build_linear_solution(alg, y, nothing, cache)
 end
 
 ## NormalBunchKaufmanFactorization
diff --git a/test/basictests.jl b/test/basictests.jl
index a6efeac85..94bbc2a3a 100644
--- a/test/basictests.jl
+++ b/test/basictests.jl
@@ -51,7 +51,7 @@ end
     @testset "Default Linear Solver" begin
         test_interface(nothing, prob1, prob2)
 
-        A1 = prob1.A
+        A1 = prob1.A * prob1.A'
         b1 = prob1.b
         x1 = prob1.u0
         y = solve(prob1)
@@ -77,9 +77,11 @@ end
         y = solve(_prob)
         @test A1 * y ≈ b1
 
-        _prob = LinearProblem(sparse(A1), b1; u0 = x1)
-        y = solve(_prob)
-        @test A1 * y ≈ b1
+        if VERSION > v"1.9-"
+            _prob = LinearProblem(sparse(A1), b1; u0 = x1)
+            y = solve(_prob)
+            @test A1 * y ≈ b1
+        end
     end
 
     @testset "UMFPACK Factorization" begin
@@ -258,19 +260,21 @@ end
         end
     end
 
-    @testset "KrylovKit" begin
-        kwargs = (; gmres_restart = 5)
-        for alg in (("Default", KrylovKitJL(kwargs...)),
-            ("CG", KrylovKitJL_CG(kwargs...)),
-            ("GMRES", KrylovKitJL_GMRES(kwargs...)))
-            @testset "$(alg[1])" begin
-                test_interface(alg[2], prob1, prob2)
+    if VERSION > v"1.9-"
+        @testset "KrylovKit" begin
+            kwargs = (; gmres_restart = 5)
+            for alg in (("Default", KrylovKitJL(kwargs...)),
+                ("CG", KrylovKitJL_CG(kwargs...)),
+                ("GMRES", KrylovKitJL_GMRES(kwargs...)))
+                @testset "$(alg[1])" begin
+                    test_interface(alg[2], prob1, prob2)
+                end
+                @test alg[2] isa KrylovKitJL
             end
-            @test alg[2] isa KrylovKitJL
         end
     end
 
-    if VERSION > v"1.7-"
+    if VERSION > v"1.9-"
         @testset "CHOLMOD" begin
             # Create a posdef symmetric matrix
             A = sprand(100, 100, 0.01)
diff --git a/test/default_algs.jl b/test/default_algs.jl
index 457d40270..d3ba54063 100644
--- a/test/default_algs.jl
+++ b/test/default_algs.jl
@@ -31,7 +31,7 @@ solve(prob)
 prob = LinearProblem(sprand(11000, 11000, 0.5), zeros(11000))
 solve(prob)
 
-@static if VERSION >= v"v1.7-"
+@static if VERSION >= v"v1.9-"
     # Test inference 
     A = rand(4, 4)
     b = rand(4)
diff --git a/test/resolve.jl b/test/resolve.jl
index 936014459..c058e527c 100644
--- a/test/resolve.jl
+++ b/test/resolve.jl
@@ -53,14 +53,16 @@ A = Symmetric([1.0 2.0
 linsolve.A = A
 @test solve!(linsolve).u ≈ [1.0, 0.0]
 
-A = Symmetric([1.0 2.0
-    2.0 1.0])
+A = [1.0 2.0
+    2.0 1.0]
+A = Symmetric(A * A')
 b = [1.0, 2.0]
 prob = LinearProblem(A, b)
 linsolve = init(prob, CholeskyFactorization(), alias_A = false, alias_b = false)
-@test solve!(linsolve).u ≈ [1.0, 0.0]
-@test solve!(linsolve).u ≈ [1.0, 0.0]
-A = Symmetric([1.0 2.0
-    2.0 1.0])
+@test solve!(linsolve).u ≈ [-1 / 3, 2 / 3]
+@test solve!(linsolve).u ≈ [-1 / 3, 2 / 3]
+A = [1.0 2.0
+    2.0 1.0]
+A = Symmetric(A * A')
 b = [1.0, 2.0]
-@test solve!(linsolve).u ≈ [1.0, 0.0]
+@test solve!(linsolve).u ≈ [-1 / 3, 2 / 3]