diff --git a/internal/ceres/block_jacobi_preconditioner.cc b/internal/ceres/block_jacobi_preconditioner.cc
index 749e0b6..29974d4 100644
--- a/internal/ceres/block_jacobi_preconditioner.cc
+++ b/internal/ceres/block_jacobi_preconditioner.cc
@@ -111,7 +111,7 @@
     }
 
     block = block.selfadjointView<Eigen::Upper>()
-                 .ldlt()
+                 .llt()
                  .solve(Matrix::Identity(size, size));
   }
   return true;
diff --git a/internal/ceres/dense_normal_cholesky_solver.cc b/internal/ceres/dense_normal_cholesky_solver.cc
index 96f5511..8e05dcc 100644
--- a/internal/ceres/dense_normal_cholesky_solver.cc
+++ b/internal/ceres/dense_normal_cholesky_solver.cc
@@ -81,7 +81,7 @@
   summary.num_iterations = 1;
   summary.termination_type = TOLERANCE;
   VectorRef(x, num_cols) =
-      lhs.selfadjointView<Eigen::Upper>().ldlt().solve(rhs);
+      lhs.selfadjointView<Eigen::Upper>().llt().solve(rhs);
   event_logger.AddEvent("Solve");
 
   return summary;
diff --git a/internal/ceres/dense_qr_solver.cc b/internal/ceres/dense_qr_solver.cc
index 1fb9709..4ab75ab 100644
--- a/internal/ceres/dense_qr_solver.cc
+++ b/internal/ceres/dense_qr_solver.cc
@@ -73,7 +73,7 @@
   event_logger.AddEvent("Setup");
 
   // Solve the system.
-  VectorRef(x, num_cols) = A->matrix().colPivHouseholderQr().solve(rhs_);
+  VectorRef(x, num_cols) = A->matrix().householderQr().solve(rhs_);
   event_logger.AddEvent("Solve");
 
   if (per_solve_options.D != NULL) {
diff --git a/internal/ceres/implicit_schur_complement.cc b/internal/ceres/implicit_schur_complement.cc
index 7c934fb..32722bb 100644
--- a/internal/ceres/implicit_schur_complement.cc
+++ b/internal/ceres/implicit_schur_complement.cc
@@ -161,7 +161,7 @@
 
     m = m
         .selfadjointView<Eigen::Upper>()
-        .ldlt()
+        .llt()
         .solve(Matrix::Identity(row_block_size, row_block_size));
   }
 }
diff --git a/internal/ceres/implicit_schur_complement_test.cc b/internal/ceres/implicit_schur_complement_test.cc
index bd36672..1694273 100644
--- a/internal/ceres/implicit_schur_complement_test.cc
+++ b/internal/ceres/implicit_schur_complement_test.cc
@@ -109,7 +109,7 @@
     solution->setZero();
     VectorRef schur_solution(solution->data() + num_cols_ - num_schur_rows,
                              num_schur_rows);
-    schur_solution = lhs->selfadjointView<Eigen::Upper>().ldlt().solve(*rhs);
+    schur_solution = lhs->selfadjointView<Eigen::Upper>().llt().solve(*rhs);
     eliminator->BackSubstitute(A_.get(), b_.get(), D,
                                schur_solution.data(), solution->data());
   }
@@ -156,7 +156,7 @@
 
     // Reference solution to the f_block.
     const Vector reference_f_sol =
-        lhs.selfadjointView<Eigen::Upper>().ldlt().solve(rhs);
+        lhs.selfadjointView<Eigen::Upper>().llt().solve(rhs);
 
     // Backsubstituted solution from the implicit schur solver using the
     // reference solution to the f_block.
diff --git a/internal/ceres/schur_complement_solver.cc b/internal/ceres/schur_complement_solver.cc
index 09f61d7..0df9304 100644
--- a/internal/ceres/schur_complement_solver.cc
+++ b/internal/ceres/schur_complement_solver.cc
@@ -135,7 +135,7 @@
   VectorRef(solution, num_rows) =
       ConstMatrixRef(m->values(), num_rows, num_rows)
       .selfadjointView<Eigen::Upper>()
-      .ldlt()
+      .llt()
       .solve(ConstVectorRef(rhs(), num_rows));
 
   return true;
diff --git a/internal/ceres/schur_eliminator_test.cc b/internal/ceres/schur_eliminator_test.cc
index a7e96ae..bed8f3a 100644
--- a/internal/ceres/schur_eliminator_test.cc
+++ b/internal/ceres/schur_eliminator_test.cc
@@ -112,7 +112,7 @@
       P.block(row, row,  block_size, block_size) =
           P
           .block(row, row,  block_size, block_size)
-          .ldlt()
+          .llt()
           .solve(Matrix::Identity(block_size, block_size));
       row += block_size;
     }
@@ -121,7 +121,7 @@
         .triangularView<Eigen::Upper>() = R - Q.transpose() * P * Q;
     rhs_expected =
         g.tail(schur_size) - Q.transpose() * P * g.head(num_eliminate_cols);
-    sol_expected = H.ldlt().solve(g);
+    sol_expected = H.llt().solve(g);
   }
 
   void EliminateSolveAndCompare(const VectorRef& diagonal,
@@ -160,7 +160,7 @@
     Vector reduced_sol  =
         lhs_ref
         .selfadjointView<Eigen::Upper>()
-        .ldlt()
+        .llt()
         .solve(rhs);
 
     // Solution to the linear least squares problem.
diff --git a/internal/ceres/schur_jacobi_preconditioner.cc b/internal/ceres/schur_jacobi_preconditioner.cc
index aa840c5..338df71 100644
--- a/internal/ceres/schur_jacobi_preconditioner.cc
+++ b/internal/ceres/schur_jacobi_preconditioner.cc
@@ -128,7 +128,7 @@
     VectorRef(y, block_size) =
         block
         .selfadjointView<Eigen::Upper>()
-        .ldlt()
+        .llt()
         .solve(ConstVectorRef(x, block_size));
 
     x += block_size;
diff --git a/internal/ceres/visibility_based_preconditioner_test.cc b/internal/ceres/visibility_based_preconditioner_test.cc
index 53d10e1..2edbb18 100644
--- a/internal/ceres/visibility_based_preconditioner_test.cc
+++ b/internal/ceres/visibility_based_preconditioner_test.cc
@@ -279,7 +279,7 @@
 //     preconditioner_->RightMultiply(x.data(), y.data());
 //     z = full_schur_complement
 //         .selfadjointView<Eigen::Upper>()
-//         .ldlt().solve(x);
+//         .llt().solve(x);
 //     double max_relative_difference =
 //         ((y - z).array() / z.array()).matrix().lpNorm<Eigen::Infinity>();
 //     EXPECT_NEAR(max_relative_difference, 0.0, kTolerance);