diff --git a/gtsam/linear/GaussianFactor.h b/gtsam/linear/GaussianFactor.h
index bb4b20e58..bc14cc670 100644
--- a/gtsam/linear/GaussianFactor.h
+++ b/gtsam/linear/GaussianFactor.h
@@ -126,7 +126,7 @@ namespace gtsam {
      * @param scatter A mapping from variable index to slot index in this HessianFactor
      * @param info The information matrix to be updated
      */
-    virtual void updateATA(const Scatter& scatter,
+    virtual void updateHessian(const Scatter& scatter,
                            SymmetricBlockMatrix* info) const = 0;
 
     /// y += alpha * A'*A*x
diff --git a/gtsam/linear/HessianFactor.cpp b/gtsam/linear/HessianFactor.cpp
index a5b3e4a9a..0cb813b01 100644
--- a/gtsam/linear/HessianFactor.cpp
+++ b/gtsam/linear/HessianFactor.cpp
@@ -248,7 +248,7 @@ HessianFactor::HessianFactor(const GaussianFactorGraph& factors,
   gttic(update);
   BOOST_FOREACH(const GaussianFactor::shared_ptr& factor, factors)
     if(factor)
-      factor->updateATA(*scatter, &info_);
+      factor->updateHessian(*scatter, &info_);
   gttoc(update);
 }
 
@@ -346,7 +346,7 @@ double HessianFactor::error(const VectorValues& c) const {
 }
 
 /* ************************************************************************* */
-void HessianFactor::updateATA(const Scatter& scatter,
+void HessianFactor::updateHessian(const Scatter& scatter,
                               SymmetricBlockMatrix* info) const {
   gttic(updateATA_HessianFactor);
   // N is number of variables in information matrix, n in HessianFactor
diff --git a/gtsam/linear/HessianFactor.h b/gtsam/linear/HessianFactor.h
index 50a81b579..160d05b15 100644
--- a/gtsam/linear/HessianFactor.h
+++ b/gtsam/linear/HessianFactor.h
@@ -344,7 +344,7 @@ namespace gtsam {
      * @param scatter A mapping from variable index to slot index in this HessianFactor
      * @param info The information matrix to be updated
      */
-    void updateATA(const Scatter& scatter, SymmetricBlockMatrix* info) const;
+    void updateHessian(const Scatter& scatter, SymmetricBlockMatrix* info) const;
 
     /** y += alpha * A'*A*x */
     void multiplyHessianAdd(double alpha, const VectorValues& x, VectorValues& y) const;
diff --git a/gtsam/linear/JacobianFactor.cpp b/gtsam/linear/JacobianFactor.cpp
index 9d0917919..c960dca04 100644
--- a/gtsam/linear/JacobianFactor.cpp
+++ b/gtsam/linear/JacobianFactor.cpp
@@ -498,7 +498,7 @@ map<Key, Matrix> JacobianFactor::hessianBlockDiagonal() const {
 }
 
 /* ************************************************************************* */
-void JacobianFactor::updateATA(const Scatter& scatter,
+void JacobianFactor::updateHessian(const Scatter& scatter,
                                SymmetricBlockMatrix* info) const {
   gttic(updateATA_JacobianFactor);
 
@@ -509,10 +509,10 @@ void JacobianFactor::updateATA(const Scatter& scatter,
   if (model && !model->isUnit()) {
     if (model->isConstrained())
       throw invalid_argument(
-          "JacobianFactor::updateATA: cannot update information with "
+          "JacobianFactor::updateHessian: cannot update information with "
           "constrained noise model");
     JacobianFactor whitenedFactor = whiten();
-    whitenedFactor.updateATA(scatter, info);
+    whitenedFactor.updateHessian(scatter, info);
   } else {
     // Ab_ is the augmented Jacobian matrix A, and we perform I += A'*A below
     // N is number of variables in information matrix, n in JacobianFactor
diff --git a/gtsam/linear/JacobianFactor.h b/gtsam/linear/JacobianFactor.h
index 73f992770..00a9b5488 100644
--- a/gtsam/linear/JacobianFactor.h
+++ b/gtsam/linear/JacobianFactor.h
@@ -278,7 +278,7 @@ namespace gtsam {
      * @param scatter A mapping from variable index to slot index in this HessianFactor
      * @param info The information matrix to be updated
      */
-    void updateATA(const Scatter& scatter, SymmetricBlockMatrix* info) const;
+    void updateHessian(const Scatter& scatter, SymmetricBlockMatrix* info) const;
 
     /** Return A*x */
     Vector operator*(const VectorValues& x) const;
diff --git a/gtsam/slam/GeneralSFMFactor.h b/gtsam/slam/GeneralSFMFactor.h
index be20ee3fa..9a8d613ad 100644
--- a/gtsam/slam/GeneralSFMFactor.h
+++ b/gtsam/slam/GeneralSFMFactor.h
@@ -149,7 +149,7 @@ namespace gtsam {
           : JacobianFactor(i1, A1, i2, A2, b, model), AC_(A1), AL_(A2), b_(b) {}
 
       // Fixed-size matrix update
-      void updateATA(const Scatter& scatter, SymmetricBlockMatrix* info) const {
+      void updateHessian(const Scatter& scatter, SymmetricBlockMatrix* info) const {
         gttic(updateATA_LinearizedFactor);
 
         // Whiten the factor if it has a noise model
@@ -157,10 +157,10 @@ namespace gtsam {
         if (model && !model->isUnit()) {
           if (model->isConstrained())
             throw std::invalid_argument(
-                "JacobianFactor::updateATA: cannot update information with "
+                "JacobianFactor::updateHessian: cannot update information with "
                 "constrained noise model");
           JacobianFactor whitenedFactor = whiten();
-          whitenedFactor.updateATA(scatter, info);
+          whitenedFactor.updateHessian(scatter, info);
         } else {
           // N is number of variables in information matrix
           DenseIndex N = info->nBlocks() - 1;
diff --git a/gtsam/slam/RegularImplicitSchurFactor.h b/gtsam/slam/RegularImplicitSchurFactor.h
index f2fc4e819..87d78911d 100644
--- a/gtsam/slam/RegularImplicitSchurFactor.h
+++ b/gtsam/slam/RegularImplicitSchurFactor.h
@@ -115,10 +115,10 @@ public:
     return D;
   }
 
-  virtual void updateATA(const Scatter& scatter,
+  virtual void updateHessian(const Scatter& scatter,
                          SymmetricBlockMatrix* info) const {
     throw std::runtime_error(
-        "RegularImplicitSchurFactor::updateATA non implemented");
+        "RegularImplicitSchurFactor::updateHessian non implemented");
   }
   virtual Matrix augmentedJacobian() const {
     throw std::runtime_error(