Ik heb geTeX'ed. En ook niet meer dan dat #leuk

Week 3/7 Linear Equation Systems.ipynb

@@ -70,7 +70,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 1,
    "metadata": {
     "deletable": false,
     "nbgrader": {
@@ -85,29 +85,7 @@
      "task": false
     }
    },
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "array([[ 1.75781401,  1.51265934, -2.74738978, -1.07039898,  0.8011521 ,\n",
-       "         1.4647544 ],\n",
-       "       [-2.71620167, -0.86457733,  0.10081129, -0.73161518, -2.78224414,\n",
-       "         0.41565052],\n",
-       "       [-0.67163289,  1.56932333,  2.48595706, -2.40628501,  0.71051658,\n",
-       "        -0.69975624],\n",
-       "       [ 1.58537064,  1.68053005,  2.06468208,  2.35512153, -0.66624755,\n",
-       "         2.62150694],\n",
-       "       [-3.14413521, -2.23161046,  1.14029891, -1.55518494,  2.72967878,\n",
-       "        -2.42673772],\n",
-       "       [-2.97430088, -2.15350692, -2.82033592,  2.92079141,  2.94935414,\n",
-       "        -0.35649436]])"
-      ]
-     },
-     "execution_count": 7,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
     "import numpy as np"
    ]
@@ -210,7 +188,32 @@
     }
    },
    "source": [
-    "YOUR ANSWER HERE"
+    "We start from our linear equations:\n",
+    "\n",
+    "$$Ax = b$$\n",
+    "\n",
+    "We seperate A into different components (diagonal, strictly lower triangular and strictly upper triangular):\n",
+    "\n",
+    "$$A = D - L - U$$\n",
+    "\n",
+    "\n",
+    "We write $D - L$ as $L'$ to get:\n",
+    "\n",
+    "\n",
+    "$$(L' - U)x = b$$\n",
+    "\n",
+    "\n",
+    "We take the iterative process of the Gauss-Seidel method to write:\n",
+    "\n",
+    "\n",
+    "$$\n",
+    "L'x^k = b + Ux^{k-1}\\\\\n",
+    "x^k = L'^{-1}(b + Ux^{k-1})\\\\\n",
+    "$$\n",
+    "If we write every component of the matrix $A$ as $a_{ij}$, we can rewrite our previous equation to:\n",
+    "\n",
+    "\n",
+    "$$x^k _i = \\frac{1}{a_{ii}}\\left[-\\sum_{j=0}^{i-1}a_{ij}x_{j}^{k} -\\sum_{j=i+1}^{n-1}a_{ij}x_{j}^{k-1} + b_i\\right].$$"
    ]
   },
   {
@@ -677,7 +680,7 @@
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "Python 3 (ipykernel)",
    "language": "python",
    "name": "python3"
   },