Update documentation

_sources/iterative/conjugategradients.ipynb

@@ -143,8 +143,20 @@
    "id": "assisted-lounge",
    "metadata": {},
    "source": [
-    "In Saad, \"Iterative Solvers\", the Preconditioned Conjugate Gradient method\n",
-    "is Algorithm 9.1, page 277. The inner products are reformulated by recursions which have better stability with respect to roundoff errors."
+    "In [Saad, \"Iterative Solvers\"](https://www-users.cse.umn.edu/~saad/IterMethBook_2ndEd.pdf), the Preconditioned Conjugate Gradient method\n",
+    "is Algorithm 9.1, page 277. The inner products are reformulated by recursions which have better stability with respect to roundoff errors.\n",
+    "\n",
+    "\n",
+    "> Given $x_0$ <br>\n",
+    "> $r_0 = b - A x_0$ <br>\n",
+    "> $p_0 = C^{-1} r_0$ <br> \n",
+    "> for $k = 0, 1, 2, \\ldots$ <br>\n",
+    "> $\\qquad \\alpha_j = \\frac{r_k^T w_k}{p_k^T A p_k}$ <br>\n",
+    "> $\\qquad x_{k+1} = x_k + \\alpha_j p_k$ <br>\n",
+    "> $\\qquad r_{k+1} = r_k - \\alpha_j A p_k$ <br>\n",
+    "> $\\qquad w_{k+1} = C^{-1} r_{k+1}$ <br>\n",
+    "> $\\qquad \\beta_k = \\frac{r_{k+1}^T w_{k+1}}{r_k^T w_k}$ <br>\n",
+    "> $\\qquad p_{k+1} = w_{k+1} + \\beta_k p_k$<br>\n"
    ]
   },
   {
@@ -180,7 +192,6 @@
     "        \n",
     "        wrn = InnerProduct(w, r)\n",
     "        err = sqrt(wrn)\n",
-    "        # print (\"Iteration\",it,\"err=\",err)\n",
     "        if callback: callback(it,err)\n",
     "        if err < tol * err0: break\n",
     "            \n",
@@ -206,7 +217,7 @@
     "a = BilinearForm(grad(u)*grad(v)*dx+10*u*v*dx).Assemble()\n",
     "f = LinearForm(x*y*v*dx).Assemble()\n",
     "gfu = GridFunction(fes)\n",
-    "pre = a.mat.CreateSmoother()   "
+    "pre = a.mat.CreateSmoother(GS=False)   "
    ]
   },
   {