diff --git a/Eigen/src/Cholesky/LDLT.h b/Eigen/src/Cholesky/LDLT.h
index a511a7dc4..8a466e1c7 100644
--- a/Eigen/src/Cholesky/LDLT.h
+++ b/Eigen/src/Cholesky/LDLT.h
@@ -97,7 +97,7 @@ void LDLT<MatrixType>::compute(const MatrixType& a)
   const int size = a.rows();
   m_matrix.resize(size, size);
   m_isPositiveDefinite = true;
-  const RealScalar eps = ei_sqrt(precision<Scalar>());
+  const RealScalar eps = precision<Scalar>() * a.cwise().abs().maxCoeff();
 
   if (size<=1)
   {