diff --git a/src/algorithms/quadratic_matrix_equation.jl b/src/algorithms/quadratic_matrix_equation.jl
index c393a2cf..721d9f8d 100644
--- a/src/algorithms/quadratic_matrix_equation.jl
+++ b/src/algorithms/quadratic_matrix_equation.jl
@@ -13,7 +13,7 @@ function solve_quadratic_matrix_equation(A::AbstractMatrix{R},
                                         initial_guess::AbstractMatrix{R} = zeros(0,0),
                                         quadratic_matrix_equation_solver::Symbol = :doubling, 
                                         timer::TimerOutput = TimerOutput(),
-                                        tol::AbstractFloat = 1e-14,
+                                        tol::AbstractFloat = 1e-12,
                                         verbose::Bool = false) where R <: Real
     sol, solved, iterations, reached_tol = solve_quadratic_matrix_equation(A, B, C, 
                                                         Val(quadratic_matrix_equation_solver), 
@@ -25,16 +25,24 @@ function solve_quadratic_matrix_equation(A::AbstractMatrix{R},
 
     if verbose println("Quadratic matrix equation solver: $quadratic_matrix_equation_solver - converged: $solved in $iterations iterations to tolerance: $reached_tol") end
 
-    if !solved && quadratic_matrix_equation_solver != :schur # try schur if previous one didn't solve it
+    if !solved # try schur if previous one didn't solve it
+        if quadratic_matrix_equation_solver == :schur
+            initial_guess = reached_tol < sqrt(tol) ? sol : zeros(0,0)
+            
+            other_algo = :doubling
+        else
+            other_algo = :schur
+        end
+        
         sol, solved, iterations, reached_tol = solve_quadratic_matrix_equation(A, B, C, 
-                                                            Val(:schur), 
+                                                            Val(other_algo), 
                                                             T; 
                                                             initial_guess = initial_guess,
                                                             tol = tol,
                                                             timer = timer,
                                                             verbose = verbose)
 
-        if verbose println("Quadratic matrix equation solver: schur - converged: $solved in $iterations iterations to tolerance: $reached_tol") end
+        if verbose println("Quadratic matrix equation solver: $other_algo - converged: $solved in $iterations iterations to tolerance: $reached_tol") end
     end
 
     return sol, solved
@@ -149,11 +157,21 @@ function solve_quadratic_matrix_equation(A::AbstractMatrix{R},
 
     X = sol[T.dynamic_order,:] * ℒ.I(length(comb))[past_not_future_and_mixed_in_comb,:]
 
-    reached_tol = ℒ.norm(A * X * X + B * X + C) / ℒ.norm(A * X * X)
+    iter = 0
+
+    AXX = A * X^2
+    
+    AXXnorm = ℒ.norm(AXX)
+    
+    ℒ.mul!(AXX, B, X, 1, 1)
+
+    ℒ.axpy!(1, C, AXX)
+    
+    reached_tol = ℒ.norm(AXX) / AXXnorm
     
     converged = reached_tol < tol
 
-    return X, converged, 0, reached_tol
+    return X, converged, iter, reached_tol
 end
 
 
@@ -313,7 +331,7 @@ function solve_quadratic_matrix_equation(A::AbstractMatrix{R},
         # println("Iter: $i; xtol: $Xtol; ytol: $Ytol; rel ytol: $relYtol; rel xtol: $relXtol")
 
         # Check for convergence
-        if Xtol < tol# && Yreltol < tol # i % 2 == 0 && 
+        if Xtol < tol / 100# && Yreltol < tol # i % 2 == 0 && 
             solved = true
             iter = i
             break
@@ -347,7 +365,7 @@ function solve_quadratic_matrix_equation(A::AbstractMatrix{R},
     
     converged = reached_tol < tol
 
-    return X_new, converged, iter, reached_tol
+    return X, converged, iter, reached_tol
 end