diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 20d458c..7a35870 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -18,6 +18,8 @@ Added
 ^^^^^
 
 * Official support for Python 3.9, 3.10, and 3.11.
+* Documented computational complexity of adding new data to an online Gaussian
+  Process.
 
 Removed
 ^^^^^^^
diff --git a/goppy/core.py b/goppy/core.py
index c3ebb6e..29ed587 100644
--- a/goppy/core.py
+++ b/goppy/core.py
@@ -120,9 +120,22 @@ def fit(self, x, y):
         self.trained = True
 
     def add(self, x, y):
-        """Adds additional training data to the Gaussian process and adjusts
+        r"""Adds additional training data to the Gaussian process and adjusts
         the fit.
 
+        The complexity of this method is in :math:`O(n \cdot \max(n^2, N^2))`
+        where
+
+        * :math:`n` is the number of data points being added,
+        * and :math:`N` is the total number of data points added so far.
+
+        This is better than re-initializing the Gaussian process, which would
+        have a complexity in :math:`O((n + N)^3)` because of the matrix
+        inversion.
+
+        `See this master's thesis for more details.
+        <https://github.com/jgosmann/goppy/files/11995181/thesis.pdf>`_
+
         Parameters
         ----------
         x : (`N`, `D`) array-like