diff --git a/internal/ceres/conjugate_gradients_solver.cc b/internal/ceres/conjugate_gradients_solver.cc
index 92e829c..d7aee31 100644
--- a/internal/ceres/conjugate_gradients_solver.cc
+++ b/internal/ceres/conjugate_gradients_solver.cc
@@ -137,7 +137,8 @@
       if (IsZeroOrInfinity(beta)) {
         summary.termination_type = LINEAR_SOLVER_FAILURE;
         summary.message = StringPrintf(
-            "Numerical failure. beta = rho_n / rho_{n-1} = %e.", beta);
+            "Numerical failure. beta = rho_n / rho_{n-1} = %e, "
+            "rho_n = %e, rho_{n-1} = %e", beta, rho, last_rho);
         break;
       }
       p = z + beta * p;
@@ -157,7 +158,8 @@
     if (IsInfinite(alpha)) {
       summary.termination_type = LINEAR_SOLVER_FAILURE;
       summary.message =
-          StringPrintf("Numerical failure. alpha = rho / pq = %e", alpha);
+          StringPrintf("Numerical failure. alpha = rho / pq = %e, "
+                       "rho = %e, pq = %e.", alpha, rho, pq);
       break;
     }
 
diff --git a/internal/ceres/levenberg_marquardt_strategy.cc b/internal/ceres/levenberg_marquardt_strategy.cc
index e47ef48..84a66f9 100644
--- a/internal/ceres/levenberg_marquardt_strategy.cc
+++ b/internal/ceres/levenberg_marquardt_strategy.cc
@@ -108,9 +108,12 @@
       linear_solver_->Solve(jacobian, residuals, solve_options, step);
 
   if (linear_solver_summary.termination_type == LINEAR_SOLVER_FATAL_ERROR) {
-    LOG(WARNING) << "Linear solver fatal error.";
-  } else if (linear_solver_summary.termination_type == LINEAR_SOLVER_FAILURE ||
-             !IsArrayValid(num_parameters, step)) {
+    LOG(WARNING) << "Linear solver fatal error: "
+                 << linear_solver_summary.message;
+  } else if (linear_solver_summary.termination_type == LINEAR_SOLVER_FAILURE)  {
+    LOG(WARNING) << "Linear solver failure. Failed to compute a step: "
+                 << linear_solver_summary.message;
+  } else if (!IsArrayValid(num_parameters, step)) {
     LOG(WARNING) << "Linear solver failure. Failed to compute a finite step.";
     linear_solver_summary.termination_type = LINEAR_SOLVER_FAILURE;
   } else {