diff --git a/internal/ceres/implicit_schur_complement_test.cc b/internal/ceres/implicit_schur_complement_test.cc
index e586ea1..21401f7 100644
--- a/internal/ceres/implicit_schur_complement_test.cc
+++ b/internal/ceres/implicit_schur_complement_test.cc
@@ -89,7 +89,8 @@
     scoped_ptr<SchurEliminatorBase> eliminator(
         SchurEliminatorBase::Create(options));
     CHECK_NOTNULL(eliminator.get());
-    eliminator->Init(num_eliminate_blocks_, bs);
+    const bool kFullRankETE = true;
+    eliminator->Init(num_eliminate_blocks_, kFullRankETE, bs);
 
     lhs->resize(num_schur_rows, num_schur_rows);
     rhs->resize(num_schur_rows);
diff --git a/internal/ceres/schur_complement_solver.cc b/internal/ceres/schur_complement_solver.cc
index 6544983..81e0d46 100644
--- a/internal/ceres/schur_complement_solver.cc
+++ b/internal/ceres/schur_complement_solver.cc
@@ -135,7 +135,9 @@
                     &options_.e_block_size,
                     &options_.f_block_size);
     eliminator_.reset(CHECK_NOTNULL(SchurEliminatorBase::Create(options_)));
-    eliminator_->Init(options_.elimination_groups[0], A->block_structure());
+    const bool kFullRankETE = true;
+    eliminator_->Init(
+        options_.elimination_groups[0], kFullRankETE, A->block_structure());
   };
   std::fill(x, x + A->num_cols(), 0.0);
   event_logger.AddEvent("Setup");
diff --git a/internal/ceres/schur_eliminator.h b/internal/ceres/schur_eliminator.h
index 761b58a..a546228 100644
--- a/internal/ceres/schur_eliminator.h
+++ b/internal/ceres/schur_eliminator.h
@@ -171,7 +171,14 @@
   // CompressedRowBlockStructure object passed to this method is the
   // same one (or is equivalent to) the one associated with the
   // BlockSparseMatrix objects below.
+  //
+  // assume_full_rank_ete controls how the eliminator inverts with the
+  // diagonal blocks corresponding to e blocks in A'A. If
+  // assume_full_rank_ete is true, then a Cholesky factorization is
+  // used to compute the inverse, otherwise a singular value
+  // decomposition is used to compute the pseudo inverse.
   virtual void Init(int num_eliminate_blocks,
+                    bool assume_full_rank_ete,
                     const CompressedRowBlockStructure* bs) = 0;
 
   // Compute the Schur complement system from the augmented linear
@@ -225,6 +232,7 @@
   // SchurEliminatorBase Interface
   virtual ~SchurEliminator();
   virtual void Init(int num_eliminate_blocks,
+                    bool assume_full_rank_ete,
                     const CompressedRowBlockStructure* bs);
   virtual void Eliminate(const BlockSparseMatrix* A,
                          const double* b,
@@ -308,7 +316,9 @@
                                int row_block_index,
                                BlockRandomAccessMatrix* lhs);
 
+  int num_threads_;
   int num_eliminate_blocks_;
+  bool assume_full_rank_ete_;
 
   // Block layout of the columns of the reduced linear system. Since
   // the f blocks can be of varying size, this vector stores the
@@ -341,7 +351,6 @@
   scoped_array<double> chunk_outer_product_buffer_;
 
   int buffer_size_;
-  int num_threads_;
   int uneliminated_row_begins_;
 
   // Locks for the blocks in the right hand side of the reduced linear
diff --git a/internal/ceres/schur_eliminator_impl.h b/internal/ceres/schur_eliminator_impl.h
index f253588..7ee419e 100644
--- a/internal/ceres/schur_eliminator_impl.h
+++ b/internal/ceres/schur_eliminator_impl.h
@@ -60,6 +60,7 @@
 #include "ceres/internal/eigen.h"
 #include "ceres/internal/fixed_array.h"
 #include "ceres/internal/scoped_ptr.h"
+#include "ceres/invert_psd_matrix.h"
 #include "ceres/map_util.h"
 #include "ceres/schur_eliminator.h"
 #include "ceres/small_blas.h"
@@ -76,14 +77,16 @@
 }
 
 template <int kRowBlockSize, int kEBlockSize, int kFBlockSize>
-void
-SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::
-Init(int num_eliminate_blocks, const CompressedRowBlockStructure* bs) {
+void SchurEliminator<kRowBlockSize, kEBlockSize, kFBlockSize>::Init(
+    int num_eliminate_blocks,
+    bool assume_full_rank_ete,
+    const CompressedRowBlockStructure* bs) {
   CHECK_GT(num_eliminate_blocks, 0)
       << "SchurComplementSolver cannot be initialized with "
       << "num_eliminate_blocks = 0.";
 
   num_eliminate_blocks_ = num_eliminate_blocks;
+  assume_full_rank_ete_ = assume_full_rank_ete;
 
   const int num_col_blocks = bs->cols.size();
   const int num_row_blocks = bs->rows.size();
@@ -268,10 +271,7 @@
     // use it to multiply other matrices/vectors instead of doing a
     // Solve call over and over again.
     typename EigenTypes<kEBlockSize, kEBlockSize>::Matrix inverse_ete =
-        ete
-        .template selfadjointView<Eigen::Upper>()
-        .llt()
-        .solve(Matrix::Identity(e_block_size, e_block_size));
+        InvertPSDMatrix<kEBlockSize>(assume_full_rank_ete_, ete);
 
     // For the current chunk compute and update the rhs of the reduced
     // linear system.
@@ -360,7 +360,8 @@
               ete.data(), 0, 0, e_block_size, e_block_size);
     }
 
-    ete.llt().solveInPlace(y_block);
+    y_block = InvertPSDMatrix<kEBlockSize>(assume_full_rank_ete_, ete)
+        * y_block;
   }
 }
 
diff --git a/internal/ceres/schur_eliminator_test.cc b/internal/ceres/schur_eliminator_test.cc
index 85ecd8f..f07d102 100644
--- a/internal/ceres/schur_eliminator_test.cc
+++ b/internal/ceres/schur_eliminator_test.cc
@@ -153,7 +153,8 @@
 
     scoped_ptr<SchurEliminatorBase> eliminator;
     eliminator.reset(SchurEliminatorBase::Create(options));
-    eliminator->Init(num_eliminate_blocks, A->block_structure());
+    const bool kFullRankETE = true;
+    eliminator->Init(num_eliminate_blocks, kFullRankETE, A->block_structure());
     eliminator->Eliminate(A.get(), b.get(), diagonal.data(), &lhs, rhs.data());
 
     MatrixRef lhs_ref(lhs.mutable_values(), lhs.num_rows(), lhs.num_cols());
diff --git a/internal/ceres/schur_jacobi_preconditioner.cc b/internal/ceres/schur_jacobi_preconditioner.cc
index 3e6cc90..c3f43a9 100644
--- a/internal/ceres/schur_jacobi_preconditioner.cc
+++ b/internal/ceres/schur_jacobi_preconditioner.cc
@@ -76,7 +76,9 @@
   eliminator_options.f_block_size = options_.f_block_size;
   eliminator_options.row_block_size = options_.row_block_size;
   eliminator_.reset(SchurEliminatorBase::Create(eliminator_options));
-  eliminator_->Init(eliminator_options.elimination_groups[0], &bs);
+  const bool kFullRankETE = true;
+  eliminator_->Init(
+      eliminator_options.elimination_groups[0], kFullRankETE, &bs);
 }
 
 // Update the values of the preconditioner matrix and factorize it.
diff --git a/internal/ceres/visibility_based_preconditioner.cc b/internal/ceres/visibility_based_preconditioner.cc
index b0000cd..429626a 100644
--- a/internal/ceres/visibility_based_preconditioner.cc
+++ b/internal/ceres/visibility_based_preconditioner.cc
@@ -341,7 +341,8 @@
   eliminator_options.f_block_size = options_.f_block_size;
   eliminator_options.row_block_size = options_.row_block_size;
   eliminator_.reset(SchurEliminatorBase::Create(eliminator_options));
-  eliminator_->Init(eliminator_options.elimination_groups[0], &bs);
+  const bool kFullRankETE = true;
+  eliminator_->Init(eliminator_options.elimination_groups[0], kFullRankETE, &bs);
 }
 
 // Update the values of the preconditioner matrix and factorize it.