diff --git a/qiskit/aqua/general/linear_systems_of_equations.ipynb b/qiskit/aqua/general/linear_systems_of_equations.ipynb
index 58e2a5e06..3d857aa4d 100644
--- a/qiskit/aqua/general/linear_systems_of_equations.ipynb
+++ b/qiskit/aqua/general/linear_systems_of_equations.ipynb
@@ -51,7 +51,7 @@
     "from qiskit.aqua import run_algorithm\n",
     "from qiskit.aqua.input import LinearSystemInput\n",
     "from qiskit.quantum_info import state_fidelity\n",
-    "from qiskit.aqua.algorithms.classical import ExactLPsolver\n",
+    "from qiskit.aqua.algorithms.classical import ExactLSsolver\n",
     "import numpy as np"
    ]
   },
@@ -147,7 +147,7 @@
     "result = run_algorithm(params)\n",
     "print(\"solution \", np.round(result['solution'], 5))\n",
     "\n",
-    "result_ref = ExactLPsolver(matrix, vector).run()\n",
+    "result_ref = ExactLSsolver(matrix, vector).run()\n",
     "print(\"classical solution \", np.round(result_ref['solution'], 5))\n",
     "\n",
     "print(\"probability %f\" % result['probability_result'])\n",
@@ -186,7 +186,7 @@
     "result = run_algorithm(params2)\n",
     "print(\"solution \", np.round(result['solution'], 5))\n",
     "\n",
-    "result_ref = ExactLPsolver(matrix, vector).run()\n",
+    "result_ref = ExactLSsolver(matrix, vector).run()\n",
     "print(\"classical solution \", np.round(result_ref['solution'], 5))\n",
     "\n",
     "print(\"probability %f\" % result['probability_result'])\n",
@@ -252,7 +252,13 @@
     "    'name': 'LinearSystemInput',\n",
     "    'matrix': matrix,\n",
     "    'vector': vector\n",
-    "}"
+    "}\n",
+    "params3['reciprocal'] = {\n",
+    "    'negative_evals': True\n",
+    "}\n",
+    "params3['eigs'] = {\n",
+    "    'negative_evals': True\n",
+    "}\n"
    ]
   },
   {
@@ -264,10 +270,10 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "solution  [0.22147+0.j 0.22034-0.j]\n",
+      "solution  [0.14223-5.e-05j 0.28622+7.e-05j]\n",
       "classical solution  [0.14286 0.28571]\n",
-      "probability 0.424639\n",
-      "fidelity 0.898454\n"
+      "probability 0.000316\n",
+      "fidelity 0.999994\n"
      ]
     }
    ],
@@ -275,7 +281,7 @@
     "result = run_algorithm(params3)\n",
     "print(\"solution \", np.round(result['solution'], 5))\n",
     "\n",
-    "result_ref = ExactLPsolver(matrix, vector).run()\n",
+    "result_ref = ExactLSsolver(matrix, vector).run()\n",
     "print(\"classical solution \", np.round(result_ref['solution'], 5))\n",
     "\n",
     "print(\"probability %f\" % result['probability_result'])\n",
@@ -286,7 +292,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Compared to the the first example, the circuit depth is increased approximately by a factor 2,5"
+    "Compared to the the first example, the circuit depth is increased approximately by a factor of 6"
    ]
   },
   {
@@ -298,8 +304,8 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "circuit_width 7\n",
-      "circuit_depth 30254\n"
+      "circuit_width 11\n",
+      "circuit_depth 73313\n"
      ]
     }
    ],
@@ -378,7 +384,7 @@
     "result = run_algorithm(params4)\n",
     "print(\"solution \", np.round(result['solution'], 5))\n",
     "\n",
-    "result_ref = ExactLPsolver(matrix, vector).run()\n",
+    "result_ref = ExactLSsolver(matrix, vector).run()\n",
     "print(\"classical solution \", np.round(result_ref['solution'], 5))\n",
     "\n",
     "print(\"probability %f\" % result['probability_result'])\n",
@@ -389,7 +395,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Considering the circuit depth, it is increased approximately by a factor 10 compared to the two dimensional matrices. The circuit width is increased by two additional qubits"
+    "Considering the circuit depth and circuit width"
    ]
   },
   {
@@ -451,26 +457,30 @@
    "outputs": [],
    "source": [
     "params5 = params\n",
-    "params5[\"reciprocal\"] = {\n",
-    "    \"name\": \"Lookup\",\n",
-    "    \"negative_evals\": True\n",
+    "params5['algorithm'] = {\n",
+    "    'truncate_powerdim': False,\n",
+    "    'truncate_hermitian': False\n",
+    "}\n",
+    "params5['reciprocal'] = {\n",
+    "    'name': 'Lookup',\n",
+    "    'negative_evals': True\n",
     "}\n",
-    "params5[\"eigs\"] = {\n",
-    "    \"expansion_mode\": \"suzuki\",\n",
-    "    \"expansion_order\": 2,\n",
-    "    \"name\": \"EigsQPE\",\n",
-    "    \"negative_evals\": True,\n",
-    "    \"num_ancillae\": 6,\n",
-    "    \"num_time_slices\": 70\n",
+    "params5['eigs'] = {\n",
+    "    'expansion_mode': 'suzuki',\n",
+    "    'expansion_order': 2,\n",
+    "    'name': 'EigsQPE',\n",
+    "    'negative_evals': True,\n",
+    "    'num_ancillae': 6,\n",
+    "    'num_time_slices': 70\n",
     "}\n",
-    "params5[\"initial_state\"] = {\n",
-    "    \"name\": \"CUSTOM\"\n",
+    "params5['initial_state'] = {\n",
+    "    'name': 'CUSTOM'\n",
     "}\n",
-    "params5[\"iqft\"] = {\n",
-    "    \"name\": \"STANDARD\"\n",
+    "params5['iqft'] = {\n",
+    "    'name': 'STANDARD'\n",
     "}\n",
-    "params5[\"qft\"] = {\n",
-    "    \"name\": \"STANDARD\"\n",
+    "params5['qft'] = {\n",
+    "    'name': 'STANDARD'\n",
     "}"
    ]
   },
@@ -521,7 +531,7 @@
     "result = hhl.run(quantum_instance)\n",
     "print(\"solution \", np.round(result['solution'], 5))\n",
     "\n",
-    "result_ref = ExactLPsolver(matrix, vector).run()\n",
+    "result_ref = ExactLSsolver(matrix, vector).run()\n",
     "print(\"classical solution \", np.round(result_ref['solution'], 5))\n",
     "\n",
     "print(\"probability %f\" % result['probability_result'])\n",