diff --git a/modules/calib3d/src/precomp.hpp b/modules/calib3d/src/precomp.hpp
index 3208680c5f..2a9fd7d004 100644
--- a/modules/calib3d/src/precomp.hpp
+++ b/modules/calib3d/src/precomp.hpp
@@ -61,6 +61,21 @@
 namespace cv
 {
 
+/**
+ * Compute the number of iterations given the confidence, outlier ratio, number
+ * of model points and the maximum iteration number.
+ *
+ * @param p confidence value
+ * @param ep outlier ratio
+ * @param modelPoints number of model points required for estimation
+ * @param maxIters maximum number of iterations
+ * @return
+ * \f[
+ * \frac{\ln(1-p)}{\ln\left(1-(1-ep)^\mathrm{modelPoints}\right)}
+ * \f]
+ *
+ * If the computed number of iterations is less than maxIters, then 1 is returned.
+ */
 int RANSACUpdateNumIters( double p, double ep, int modelPoints, int maxIters );
 
 class CV_EXPORTS LMSolver : public Algorithm
diff --git a/modules/core/include/opencv2/core.hpp b/modules/core/include/opencv2/core.hpp
index a6fa49c7eb..a3f3740776 100644
--- a/modules/core/include/opencv2/core.hpp
+++ b/modules/core/include/opencv2/core.hpp
@@ -1739,20 +1739,21 @@ element is a 2D/3D vector to be transformed.
 */
 CV_EXPORTS_W void perspectiveTransform(InputArray src, OutputArray dst, InputArray m );
 
-/** @brief Copies the lower or the upper half of a square matrix to another half.
+/** @brief Copies the lower or the upper half of a square matrix to its another half.
 
-The function cv::completeSymm copies the lower half of a square matrix to
+The function cv::completeSymm copies the lower or the upper half of a square matrix to
 its another half. The matrix diagonal remains unchanged:
-*   \f$\texttt{mtx}_{ij}=\texttt{mtx}_{ji}\f$ for \f$i > j\f$ if
+ - \f$\texttt{m}_{ij}=\texttt{m}_{ji}\f$ for \f$i > j\f$ if
     lowerToUpper=false
-*   \f$\texttt{mtx}_{ij}=\texttt{mtx}_{ji}\f$ for \f$i < j\f$ if
+ - \f$\texttt{m}_{ij}=\texttt{m}_{ji}\f$ for \f$i < j\f$ if
     lowerToUpper=true
-@param mtx input-output floating-point square matrix.
+
+@param m input-output floating-point square matrix.
 @param lowerToUpper operation flag; if true, the lower half is copied to
 the upper half. Otherwise, the upper half is copied to the lower half.
 @sa flip, transpose
 */
-CV_EXPORTS_W void completeSymm(InputOutputArray mtx, bool lowerToUpper = false);
+CV_EXPORTS_W void completeSymm(InputOutputArray m, bool lowerToUpper = false);
 
 /** @brief Initializes a scaled identity matrix.