diff --git a/algo.py b/algo.py
index eb8952a..6e72749 100644
--- a/algo.py
+++ b/algo.py
@@ -311,7 +311,7 @@ def pagerank_numpy(G, alpha=0.85, personalization=None, weight="weight", danglin
     return dict(zip(G, map(float, largest / norm)))
 
 
-def pagerank(G, alpha=0.85, personalization=None, max_iter=10000, tol=1.0e-9, nstart=None, weight="weight", dangling=None,):
+def pagerank(G, alpha=0.85, personalization=None, max_iter=1000, tol=1.0e-8, nstart=None, weight="weight", dangling=None,):
 
     """
     Returns the PageRank of the nodes in the graph. Slighly modified NetworkX implementation.
@@ -427,7 +427,7 @@ def pagerank(G, alpha=0.85, personalization=None, max_iter=10000, tol=1.0e-9, ns
     raise nx.PowerIterationFailedConvergence(max_iter)
 
 
-def shifted_pow_pagerank(G, alphas=[0.85, 0.9, 0.95, 0.99], max_iter=10000, tol=1.0e-9):
+def shifted_pow_pagerank(G, alphas=[0.85, 0.9, 0.95, 0.99], max_iter=1000, tol=1.0e-8):
 
     """
     Compute the PageRank of each node in the graph G. Algorithm 1 in the paper [1].
@@ -492,8 +492,9 @@ def shifted_pow_pagerank(G, alphas=[0.85, 0.9, 0.95, 0.99], max_iter=10000, tol=
 
     for i in range(len(alphas)):
         r[:,[i]] = alphas[i] * mu # residual vector for the i-th alpha
-        # r_i = r[:,[i]].toarray()
-        res[i] = sp.sparse.linalg.norm(r[:,[i]]) # residual norm for the i-th alpha
+        r_i = r[:,[i]].toarray()
+        # res[i] = sp.sparse.linalg.norm(r[:,[i]]) # residual norm for the i-th alpha
+        res [i] = np.linalg.norm(r_i, ord = 2) # residual norm for the i-th alpha
         if res[i] >= tol:
             x[:, [i]] = r[:,[i]] + v # update the i-th column of x
             
@@ -503,18 +504,20 @@ def shifted_pow_pagerank(G, alphas=[0.85, 0.9, 0.95, 0.99], max_iter=10000, tol=
         err = np.max(res) 
         # print("Error: ", err)
         if err < tol:
-            print("Convergence reached with, ", mv, " matrix-vector multiplications")
+            # print("Convergence reached with, ", mv, " matrix-vector multiplications")
             return x, mv, alphas, tol
 
         # print("Iteration: ", _, "\r", end="")
 
         mu = A @ mu
         mv += 1
+        print("\nCurrent number of matrix-vector products: ", mv, "\r", end="")
         for i in range(len(alphas)):
             if res[i] >= tol:
                 r[:,[i]] = np.power(alphas[i], mv+1) * mu
-                # r_i = r[:,[i]].toarray()
-                res[i] = sp.sparse.linalg.norm(r[:,[i]])
+                r_i = r[:,[i]].toarray()
+                # res[i] = sp.sparse.linalg.norm(r[:,[i]])
+                res[i] = np.linalg.norm(r_i, ord = 2)
 
                 if res[i] >= tol:
                     x[:, [i]] = r[:,[i]] + v
diff --git a/testing/shifted_GMRES.ipynb b/testing/shifted_GMRES.ipynb
index a857195..018d11a 100644
--- a/testing/shifted_GMRES.ipynb
+++ b/testing/shifted_GMRES.ipynb
@@ -177,8 +177,9 @@
     "    # compute the residual vector and the norm of each col in the vector res\n",
     "    for i in range(len(a)):\n",
     "        r[:,[i]] = ((1 - a[i])/a[i])*v - ((1/a[i])*I - Pt).dot(x[:,[i]])\n",
-    "        res[i] = sp.sparse.linalg.norm(r[:,[i]], ord='fro') # frobenius norm since l2 norm is not defined for sparse matrices in scipy\n",
-    "\n",
+    "        r_i = r[:,[i]].toarray()   # r_i is the residual vector for alpha_i\n",
+    "        res[i] = a[i] * np.linalg.norm(r_i, ord = 2)\n",
+    "        \n",
     "    for _ in range(maxit):\n",
     "        err = np.absolute(np.max(res)) # check if we have converged\n",
     "        if err < tau:\n",
@@ -187,11 +188,11 @@
     "\n",
     "        print(\"\\niter = \", iter)\n",
     "        print(\"res: \", res)\n",
-    "        print(\"err = \", err)\n",
+    "        # print(\"err = \", err)\n",
     "\n",
     "        # find k as the index of the largest residual\n",
     "        k = int(np.argmax(res))\n",
-    "        print(\"k = \", k)\n",
+    "        # print(\"k = \", k)\n",
     "\n",
     "        # compute gamma as defined in the paper\n",
     "        gamma = compute_gamma(res, a, k)\n",
@@ -202,6 +203,7 @@
     "        H = H[:-1,:] # remove the last row of H\n",
     "        V = V[:,:-1] # remove the last col of V\n",
     "        mv = mv + j # update the number of matrix-vector products\n",
+    "        print(\"mv = \", mv)\n",
     "\n",
     "        H_e1 = np.zeros(H.shape[0]) \n",
     "        H_e1[0] = 1 # canonical vector e1 of size H.shape[0]\n",
@@ -221,25 +223,30 @@
     "        V_e1 = sp.sparse.lil_matrix(V_e1) # canonical vector e1 of size V.shape[0]\n",
     "\n",
     "        # Update res[k]\n",
-    "        res[k] = a[k]* (sp.sparse.linalg.norm(beta*V_e1.T - V @ y[:,[k]]))\n",
+    "        tmp = beta*V_e1.T - V @ y[:,[k]]\n",
+    "        tmp = tmp.toarray()\n",
+    "        res[k] = a[k] * np.linalg.norm(tmp, ord = 2)\n",
+    "        # res[k] = a[k]* (sp.sparse.linalg.norm(beta*V_e1.T - V @ y[:,[k]]))\n",
     "\n",
     "        # multi shift\n",
+    "        H_new = H\n",
     "        for i in range(len(a)):\n",
-    "            if i != k and res[i] >= tau:\n",
+    "            if i != k:\n",
     "                if res[i] >= tau:\n",
     "                    \n",
-    "                    H = H + ((1-a[i])/a[i] - (1-a[k])/a[k])*sp.sparse.eye(H.shape[0], H.shape[1], format='lil')\n",
+    "                    # H = H + ((1-a[i])/a[i] - (1-a[k])/a[k])*sp.sparse.eye(H.shape[0], H.shape[1], format='lil')\n",
+    "                    H_new = H + ((1-a[i])/a[i] - (1-a[k])/a[k])*sp.sparse.eye(H.shape[0], H.shape[1], format='lil')\n",
     "\n",
     "                    # Compute z as described in the paper\n",
     "                    z1 = H_e1.T*beta\n",
     "                    z1 = z1.reshape(z1.shape[0],1)\n",
-    "                    z2 = H @ y[:,[1]]\n",
+    "                    z2 = H @ y[:,[k]]\n",
     "                    z2 = z2.reshape(z2.shape[0],1)\n",
     "                    z = z1 - z2\n",
     "\n",
     "                    # Solve the linear system for A and b\n",
-    "                    A = sp.sparse.hstack([H, z])\n",
-    "                    b = (beta*H_e1)\n",
+    "                    A = sp.sparse.hstack([H_new, z])\n",
+    "                    b = gamma[i]*(beta*H_e1)\n",
     "\n",
     "                    to_split = sp.sparse.linalg.lsqr(A, b.reshape(b.shape[0],1))[0]\n",
     "                    \n",
@@ -253,9 +260,9 @@
     "                    # update res[i]\n",
     "                    res[i] = (a[i]/a[k])*gamma[i]*res[k]\n",
     "\n",
-    "                else:\n",
-    "                    if res[i] < tau:\n",
-    "                        print(\"res[\", i, \"] is smaller than tau = \", tau, \" at iteration \", iter)\n",
+    "                # else:\n",
+    "                #     if res[i] < tau:\n",
+    "                #         print(\"res[\", i, \"] is smaller than tau = \", tau, \" at iteration \", iter)\n",
     "\n",
     "        iter += 1\n",
     "        x = x_new\n",
@@ -295,504 +302,404 @@
      "text": [
       "\n",
       "iter =  1\n",
-      "res:  [0.00558049 0.00351364 0.00166436 0.00031942]\n",
-      "err =  0.005580489988532435\n",
-      "k =  0\n",
+      "res:  [0.00474342 0.00316228 0.00158114 0.00031623]\n",
+      "mv =  99\n",
       "\n",
       "iter =  2\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  198\n",
       "\n",
       "iter =  3\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  297\n",
       "\n",
       "iter =  4\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  396\n",
       "\n",
       "iter =  5\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  495\n",
       "\n",
       "iter =  6\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  594\n",
       "\n",
       "iter =  7\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  693\n",
       "\n",
       "iter =  8\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  792\n",
       "\n",
       "iter =  9\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  891\n",
       "\n",
       "iter =  10\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  990\n",
       "\n",
       "iter =  11\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  1089\n",
       "\n",
       "iter =  12\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  1188\n",
       "\n",
       "iter =  13\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  1287\n",
       "\n",
       "iter =  14\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  1386\n",
       "\n",
       "iter =  15\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  1485\n",
       "\n",
       "iter =  16\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  1584\n",
       "\n",
       "iter =  17\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  1683\n",
       "\n",
       "iter =  18\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  1782\n",
       "\n",
       "iter =  19\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  1881\n",
       "\n",
       "iter =  20\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  1980\n",
       "\n",
       "iter =  21\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  2079\n",
       "\n",
       "iter =  22\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  2178\n",
       "\n",
       "iter =  23\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  2277\n",
       "\n",
       "iter =  24\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  2376\n",
       "\n",
       "iter =  25\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  2475\n",
       "\n",
       "iter =  26\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  2574\n",
       "\n",
       "iter =  27\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  2673\n",
       "\n",
       "iter =  28\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  2772\n",
       "\n",
       "iter =  29\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  2871\n",
       "\n",
       "iter =  30\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  2970\n",
       "\n",
       "iter =  31\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  3069\n",
       "\n",
       "iter =  32\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  3168\n",
       "\n",
       "iter =  33\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  3267\n",
       "\n",
       "iter =  34\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  3366\n",
       "\n",
       "iter =  35\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  3465\n",
       "\n",
       "iter =  36\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  3564\n",
       "\n",
       "iter =  37\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  3663\n",
       "\n",
       "iter =  38\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  3762\n",
       "\n",
       "iter =  39\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  3861\n",
       "\n",
       "iter =  40\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  3960\n",
       "\n",
       "iter =  41\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  4059\n",
       "\n",
       "iter =  42\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  4158\n",
       "\n",
       "iter =  43\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  4257\n",
       "\n",
       "iter =  44\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  4356\n",
       "\n",
       "iter =  45\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  4455\n",
       "\n",
       "iter =  46\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  4554\n",
       "\n",
       "iter =  47\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  4653\n",
       "\n",
       "iter =  48\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  4752\n",
       "\n",
       "iter =  49\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  4851\n",
       "\n",
       "iter =  50\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  4950\n",
       "\n",
       "iter =  51\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  5049\n",
       "\n",
       "iter =  52\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  5148\n",
       "\n",
       "iter =  53\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  5247\n",
       "\n",
       "iter =  54\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  5346\n",
       "\n",
       "iter =  55\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  5445\n",
       "\n",
       "iter =  56\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  5544\n",
       "\n",
       "iter =  57\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  5643\n",
       "\n",
       "iter =  58\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  5742\n",
       "\n",
       "iter =  59\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  5841\n",
       "\n",
       "iter =  60\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  5940\n",
       "\n",
       "iter =  61\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  6039\n",
       "\n",
       "iter =  62\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  6138\n",
       "\n",
       "iter =  63\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  6237\n",
       "\n",
       "iter =  64\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  6336\n",
       "\n",
       "iter =  65\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  6435\n",
       "\n",
       "iter =  66\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  6534\n",
       "\n",
       "iter =  67\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  6633\n",
       "\n",
       "iter =  68\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  6732\n",
       "\n",
       "iter =  69\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  6831\n",
       "\n",
       "iter =  70\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  6930\n",
       "\n",
       "iter =  71\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  7029\n",
       "\n",
       "iter =  72\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  7128\n",
       "\n",
       "iter =  73\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  7227\n",
       "\n",
       "iter =  74\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  7326\n",
       "\n",
       "iter =  75\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  7425\n",
       "\n",
       "iter =  76\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  7524\n",
       "\n",
       "iter =  77\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  7623\n",
       "\n",
       "iter =  78\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  7722\n",
       "\n",
       "iter =  79\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  7821\n",
       "\n",
       "iter =  80\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  7920\n",
       "\n",
       "iter =  81\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  8019\n",
       "\n",
       "iter =  82\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  8118\n",
       "\n",
       "iter =  83\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  8217\n",
       "\n",
       "iter =  84\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  8316\n",
       "\n",
       "iter =  85\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  8415\n",
       "\n",
       "iter =  86\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  8514\n",
       "\n",
       "iter =  87\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  8613\n",
       "\n",
       "iter =  88\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  8712\n",
       "\n",
       "iter =  89\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  8811\n",
       "\n",
       "iter =  90\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  8910\n",
       "\n",
       "iter =  91\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  9009\n",
       "\n",
       "iter =  92\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  9108\n",
       "\n",
       "iter =  93\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  9207\n",
       "\n",
       "iter =  94\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  9306\n",
       "\n",
       "iter =  95\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  9405\n",
       "\n",
       "iter =  96\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  9504\n",
       "\n",
       "iter =  97\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  9603\n",
       "\n",
       "iter =  98\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  9702\n",
       "\n",
       "iter =  99\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n",
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  9801\n",
       "\n",
       "iter =  100\n",
-      "res:  [ 6.30826211e-03  1.27202498e-07 -1.07175457e-08 -1.83681405e-08]\n",
-      "err =  0.006308262114154177\n",
-      "k =  0\n"
+      "res:  [6.34461791e-03 4.87903407e-15 3.33091494e-15 6.31758417e-16]\n",
+      "mv =  9900\n"
      ]
     },
     {
@@ -803,7 +710,7 @@
       "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
       "\u001b[0;31mException\u001b[0m                                 Traceback (most recent call last)",
       "Cell \u001b[0;32mIn[7], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m x, \u001b[38;5;28miter\u001b[39m, mv \u001b[38;5;241m=\u001b[39m \u001b[43mAlgo4\u001b[49m\u001b[43m(\u001b[49m\u001b[43mPt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mv\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m100\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43ma\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m1e-6\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m100\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m)\u001b[49m\n",
-      "Cell \u001b[0;32mIn[5], line 101\u001b[0m, in \u001b[0;36mAlgo4\u001b[0;34m(Pt, v, m, a, tau, maxit, x)\u001b[0m\n\u001b[1;32m     98\u001b[0m     \u001b[38;5;28miter\u001b[39m \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\n\u001b[1;32m     99\u001b[0m     x \u001b[38;5;241m=\u001b[39m x_new\n\u001b[0;32m--> 101\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mMaximum number of iterations reached\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
+      "Cell \u001b[0;32mIn[5], line 108\u001b[0m, in \u001b[0;36mAlgo4\u001b[0;34m(Pt, v, m, a, tau, maxit, x)\u001b[0m\n\u001b[1;32m    105\u001b[0m     \u001b[38;5;28miter\u001b[39m \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\n\u001b[1;32m    106\u001b[0m     x \u001b[38;5;241m=\u001b[39m x_new\n\u001b[0;32m--> 108\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mException\u001b[39;00m(\u001b[38;5;124m'\u001b[39m\u001b[38;5;124mMaximum number of iterations reached\u001b[39m\u001b[38;5;124m'\u001b[39m)\n",
       "\u001b[0;31mException\u001b[0m: Maximum number of iterations reached"
      ]
     }