diff --git a/include/ceres/covariance.h b/include/ceres/covariance.h
index 245381a..35fde4d 100644
--- a/include/ceres/covariance.h
+++ b/include/ceres/covariance.h
@@ -202,9 +202,9 @@
   struct CERES_EXPORT Options {
     Options()
 #ifndef CERES_NO_SUITESPARSE
-        : algorithm_type(SPARSE_QR),
+        : algorithm_type(SUITE_SPARSE_QR),
 #else
-        : algorithm_type(DENSE_SVD),
+        : algorithm_type(EIGEN_SPARSE_QR),
 #endif
           min_reciprocal_condition_number(1e-14),
           null_space_rank(0),
@@ -229,47 +229,22 @@
     //    for small to moderate sized problems. It can handle
     //    full-rank as well as rank deficient Jacobians.
     //
-    // 2. SPARSE_CHOLESKY uses the CHOLMOD sparse Cholesky
-    //    factorization library to compute the decomposition :
-    //
-    //      R'R = J'J
-    //
-    //    and then
-    //
-    //      [J'J]^-1  = [R'R]^-1
-    //
-    //    It a fast algorithm for sparse matrices that should be used
-    //    when the Jacobian matrix J is well conditioned. For
-    //    ill-conditioned matrices, this algorithm can fail
-    //    unpredictabily. This is because Cholesky factorization is
-    //    not a rank-revealing factorization, i.e., it cannot reliably
-    //    detect when the matrix being factorized is not of full
-    //    rank. SuiteSparse/CHOLMOD supplies a heuristic for checking
-    //    if the matrix is rank deficient (cholmod_rcond), but it is
-    //    only a heuristic and can have both false positive and false
-    //    negatives.
-    //
-    //    Recent versions of SuiteSparse (>= 4.2.0) provide a much
-    //    more efficient method for solving for rows of the covariance
-    //    matrix. Therefore, if you are doing SPARSE_CHOLESKY, we
-    //    strongly recommend using a recent version of SuiteSparse.
-    //
-    // 3. SPARSE_QR uses the SuiteSparseQR sparse QR factorization
-    //    library to compute the decomposition
+    // 2. EIGEN_SPARSE_QR uses the sparse QR factorization algorithm
+    //    in Eigen to compute the decomposition
     //
     //      Q * R = J
     //
     //    [J'J]^-1 = [R*R']^-1
     //
-    //    It is a moderately fast algorithm for sparse matrices, which
-    //    at the price of more time and memory than the
-    //    SPARSE_CHOLESKY algorithm is numerically better behaved and
-    //    is rank revealing, i.e., it can reliably detect when the
-    //    Jacobian matrix is rank deficient.
+    //    It is a moderately fast algorithm for sparse matrices.
     //
-    // Neither SPARSE_CHOLESKY or SPARSE_QR are capable of computing
-    // the covariance if the Jacobian is rank deficient.
-
+    // 3. SUITE_SPARSE_QR uses the SuiteSparseQR sparse QR
+    //    factorization algorithm. It uses dense linear algebra and is
+    //    multi threaded, so for large sparse sparse matrices it is
+    //    significantly faster than EIGEN_SPARSE_QR.
+    //
+    // Neither EIGEN_SPARSE_QR not SUITE_SPARSE_QR are capable of
+    // computing the covariance if the Jacobian is rank deficient.
     CovarianceAlgorithmType algorithm_type;
 
     // If the Jacobian matrix is near singular, then inverting J'J
@@ -295,29 +270,13 @@
     //    where min_sigma and max_sigma are the minimum and maxiumum
     //    singular values of J respectively.
     //
-    // 2. SPARSE_CHOLESKY
-    //
-    //      cholmod_rcond < min_reciprocal_conditioner_number
-    //
-    //    Here cholmod_rcond is a crude estimate of the reciprocal
-    //    condition number of J'J by using the maximum and minimum
-    //    diagonal entries of the Cholesky factor R. There are no
-    //    theoretical guarantees associated with this test. It can
-    //    give false positives and negatives. Use at your own
-    //    risk. The default value of min_reciprocal_condition_number
-    //    has been set to a conservative value, and sometimes the
-    //    Covariance::Compute may return false even if it is possible
-    //    to estimate the covariance reliably. In such cases, the user
-    //    should exercise their judgement before lowering the value of
-    //    min_reciprocal_condition_number.
-    //
-    // 3. SPARSE_QR
+    // 2. SUITE_SPARSE_QR and EIGEN_SPARSE_QR
     //
     //      rank(J) < num_col(J)
     //
     //   Here rank(J) is the estimate of the rank of J returned by the
-    //   SuiteSparseQR algorithm. It is a fairly reliable indication
-    //   of rank deficiency.
+    //   sparse QR factorization algorithm. It is a fairly reliable
+    //   indication of rank deficiency.
     //
     double min_reciprocal_condition_number;
 
@@ -352,8 +311,8 @@
     //
     //   lambda_i / lambda_max < min_reciprocal_condition_number.
     //
-    // This option has no effect on the SPARSE_CHOLESKY or SPARSE_QR
-    // algorithms.
+    // This option has no effect on the SUITE_SPARSE_QR and
+    // EIGEN_SPARSE_QR algorithms.
     int null_space_rank;
 
     int num_threads;
diff --git a/include/ceres/types.h b/include/ceres/types.h
index ba31236..5fccd03 100644
--- a/include/ceres/types.h
+++ b/include/ceres/types.h
@@ -399,8 +399,7 @@
 
 enum CovarianceAlgorithmType {
   DENSE_SVD,
-  SPARSE_CHOLESKY,
-  SPARSE_QR,
+  SUITE_SPARSE_QR,
   EIGEN_SPARSE_QR
 };