{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# The idea of Newton's method\n",
"\n",
"Suppose we want to find a root of the function"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"using Plots"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=1}"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f = x -> x*exp(x) - 2\n",
"\n",
"plot(f,0,1.5,label=\"function\",grid=:y,xlabel=\"x\",ylabel=\"y\",legend=:topleft)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the graph, it is clear that there is a root near $x=1$. So we call that our initial guess, $x_1$."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=2}"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x1 = 1\n",
"f1 = f(x1)\n",
"scatter!([x1],[f1],label=\"initial point\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we can compute the tangent line at the point $\\bigl(x_1,f(x_1)\\bigr)$, using the derivative."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAlgAAAGQCAIAAAD9V4nPAAAABmJLR0QA/wD/AP+gvaeTAAAgAElEQVR4nOzdd0CU9R8H8O9zA5ApW5YiSxRFEQeI5gQVBVepZaaWabltoWUu3CNT0xI1yzJnljMHylDQEEQ2ioIgS2SIbO6e5/n9ccWPFAXh7nnujvfrr+O5h+f54Lg33+e7KJZlCQAAQGsl4LsAAAAAPiEIAQCgVUMQAgBAq4YgBACAVg1BCAAArRqCEAAAWjUEIQAAtGoIQgAAaNUQhAAA0KohCAEAoFVToiAsKSnJysriuwoAAOACzZK0UqVY41OJgvDMmTPLli3juwoAAODCnhRm1nWa7yoIIUTEdwEAANDqFNWQ1bH0pZFKkUFK1CIEAIBW4rO/6akOAlcjiu9CCEGLEAAAOBb5mL2YzaS8Kea7kH+gRQgAANyhWTI3kt7mITTQ4LuUf3EdhCzLTpkyZeTIkRzfFwAAlMGuZEZfTCbaKVEzjOtHo3v27ElMTCwsLOT4vgAAwLvHVWTtHTp0lEgp+gb/xWkm5+Tk7N69e9WqVVzeFAAAlMTnf9MznASd2ypVDnLbIpw5c+aaNWu0tbW5vCkAACiD6/lsaB6b/KbSDdLkrqADBw4YGhr6+/sHBwe/7JzTp0/r6OjUPzJ58uRvv/1W8dUBAIACSRky57rm2u4StrqqrJq7+2prawuFwlefw1EQFhcXf/311ydOnEhPT8/Ly5NKpenp6TY2NmLxf4bP+vr6BgUF1T8iFos1NTW5KRIAABRkWyJjrsNM7aLT+Kmc4ygIS0tL27VrN2/ePELIs2fPSkpKJk6ceOrUKSsrq/9UIxLp6upyUxIAAHDjcRVZf4cOH610D0VlOCqrY8eO0dHRstfBwcHTpk2r+xIAANTbJzfpD50Fzko2RqYOD/ncpk2b9u3bc39fAADg3rV89vpjNmiAkjYHCS8ry3h5ed24cYP7+wIAAMekDJkXSW/zEOgobw5iiTUAAFCYb5OYdm3IeFulzholzmgAAFBl2RXsxjg60k/Zg0apUxoAAFTXxxH0Aheho4GSjpGpo+xBDQAAquiX+8yjcnJymAo0txCEAAAgZ0+qSUAUfcZHJFaBHFT9IDx79uzXX3/NdxWtyKhRo9asWcN3FQCg1D6OoD/oJHA3UfaHojIqH4TFxcXW1tarV6/mu5BW4fz58ykpKXxXAQBK7Vg6k1TC/jpIZfJFZQp9BUNDQzc3N76raBWSkpIQhADwCkU1ZNFN+vhQkVYjK10rEVV4fAsAACpifiT9roPAy1w1HorKqEOLEAAAlMHZLDamkN2vxKupNUjFygUAAOVUWkvmRNC/Dha2UbVgwaNRAACQg0U36bG21BvtVOmhqIyqBTcAACifK7lsaB6bMF4lM0UliwYAAOXxTELeD6f3DhDqivkupVnwaBQAAFrki7/pEdaUj5XqPRSVQYsQAACaLzSPPfeITZigwmmCFqFC3Lp1a+DAgfb29i3ZgjguLq66ulr2ev369Zs3b5ZTdQAA8lEpJR9eo3f1E7TV4LuUFkAQKkRAQMDUqVPv37/v6enZ7IsMGzYsKytL9rpv3759+vSRU3UAAPLxZTTtZU75d1DtKFHhxqzSOn/+/N27dwsKCk6ePDlhwoTw8HA7Oztra2tCyMOHD3Nycjp16hQTE9OtW7cjR47o6Oi88847enp6hJAHDx4EBwc/e/bM3d1dQ0OjpqbmwoULcXFxHh4eRkZGFEURQp48eXLq1Kny8vIhQ4a4uroSQoKDg11cXK5du5aZmTl48OBevXrx++MDQCtxo4A9kcHGq+ZI0fpUO8aV06NHj2pra3NycjIyMgghgYGBN2/elL0VFha2efPmu3fvTps2bdq0abW1tefOnfP19SWEnDlzpl+/fpmZmSKRaNeuXfn5+QzDPHr0KD09vaKi4tChQ0ePHs3MzOzevXtsbGxVVZWPj8/Ro0cJIUuXLvX3979x40ZFRcWwYcP+/vtvHn92AGglamgyM5ze4Skw0uS7lBZT+SRv0EfX6fwqju61p7/QvM1/jsyePfubb76ZOnWqh4fHy77r6dOnhw4dMjMzq66uNjExycnJmTt37t69e/39/QkhixcvJoR8/PHHH374oZOTU913bdiwwd/ff9euXYQQFxeXefPmTZo0iRDi5+e3fPlyQkhZWdnvv//et29fhfyoAAD/Wh5DuxpT423VoTWlnkE4oaOgQspycy+9Zs2bad++vZmZGSFES0vLzMwsNTU1Ozvbx8fn1d+VkJAwd+5c2evBgwc/evSopKSEEFL3ONTGxubOnTvNKQgAoMlii9iDaUzceNWcNvgC9QxCbyuKEGWZ0SIUCmmalr2uGwUqEv3/T56iKLFYzLJsbW2tlpbWKy6lqalZW1sre11TU0NRlIaGRv2ryfoRAQAUp5Yh74XS33oKzdo0frJKUIdWrZKztrZOTEwkhLAse/bs2QbP0dXV7dWr1/79+2VfyoLTwMDg6dOn9U/z8vI6fvw4y7KEkKNHj7q5ueno6Ci2egCA/1oTS3fUoybZqU98qGeLUKnMmTPH29s7Li6uoKDAwsJCFmMv2r9///jx48+dO2dmZnb79u3U1NQZM2aMGzeuU6dOsv4/Qsinn346atQoDw8PCwuL6OjokydPcvhzAACQ+GL2hxQmdhxv2ZFX/thC11y+10QQKkRwcLCsC5AQ0rNnz9TU1MTEREdHRwMDg4qKirZt2168eLHu5NDQUDMzM01NzaSkpISEhIqKCtm8iK+++mrhwoUFBQVmZmaurq4URRkYGISFhSUlJZWXl3fv3l3WHPzzzz+NjIxkl5o+ffo777zD+Y8LAK2ClCHvh9Nb+gqtdPjphTmS8sfJu+cOjt6lJZLnWFUEoULY2NjU/9LU1HTw4MGy17Ipg/VPqHutqan53CxAXV1dXV3d+keEQqEsJutYWVnVvTYwMJBD9QAADdkQx5i1Ie858vBQlGGZHdF74woSd3qvl28KEgQhAAA0RepTdmcyHT2Wn9QoriqpkFTu8tmkLZb/EB0EIQAANIJhycxrdKC70Ianh6Im2sZf9VusoIurz7AfAABQkG8SGQ0B+dBZPSMDLcL/y8rKOnToUNydOzXV1Y6dOk2YMAFLtAAA3CtlN8bRN/1FHDcGo3Jva4g0eph1VfSN1DPem2Hz5s0O9vZBWzcyiRHa6bevHD7g4eExeeLEysrK173U22+/nZaW9uLxBw8eTJw4kRBSUlJSN4li3bp1Dc6CiI6Onj179uveWua9995LTk5+8ThN06Wlpc27JgC0TgxLPrxGL3cT2utzmoOn0y6sv7ldRHHRWkOLkBBCvvvuu6+WLl032HliFyvBv4uz3M5/+vHFv6a8/fYfp0691tUcHBwaXCBGS0vLwcFBIpEYGRk9e/ZMNnzU0tKybvJDfSUlJTExMa//oxBCiJ2dXZs2DfQnp6SkDB8+PCcnp3mXBYBWaFcyI2HI3C7ctZpYwv4Uf+Tyw9Adw9bZ6Fs1/g0thiAkz549+2rpkqVejpNdrOsf79mu7X7fbqOPnA0ODh42bFjTLzh27FgjI6O0tDRjY+OsrKyUlJQ+ffrY29sbGhqOHz8+NTWVEHLnzh1tbW0nJycvLy9dXV2WZePi4pKTkw0NDd94440G14spLi4uLi7W09MLCQnp0KFD3U6Hz549i4yMrKmp8fLyMjExIYSMGTPGxMTk/v37hoaGOTk5iYmJvXv3dnR0TE1NlUgksnx1dXUVi9VknUAAUJD0MjYwlr7uJxJw1RqU0JL1N7c/rijYPXxTW02O5oMhCMnFixelEsnUbtYvvtXVVN+rg+nvv//+WkH41ltvnThxYunSpRKJRFtb29LScs6cORcuXNDS0ho/fvyHH35ICDlw4IBYLP70008DAwP79OnTtm3bw4cPd+7cOSsra/78+Q1upXT+/Pl169bp6en169dv9erVPj4+3377bUZGxtChQ3v16qWjo/PRRx+dPn26d+/eb7/99oEDB9atW1dRUaGlpWVjYzN37twzZ86cOnWqoqIiKCiIELJ582YEIQC8As2S90LppT2ETgYcxeCzmrKvwtcZabXdNnSNhpC7Pe8RhCQ9Pb2jkZ6WSNjgu86GbdLupjTvyra2tj/++CMhxNTU9Oeff5b1+S1ZsmT58uXbt2+XPRqVeffdd6dOnSp7PWvWrAMHDnTv3v3FC2ZmZqanp5ubmxcXF9vZ2c2ePXvDhg2jR4/esWMHIWTLli2fffZZWFhY3fkWFhaHDh0ihFhZWR04cCAgIODq1at79uxp3o8DAK3KujtMGxFZ6MLdQ9GlYYE9zbu/3/0dittdEzBYhgiFQvol638SQqQMKxY38xeTQYMGyV44OTnl5ua+4szi4uIFCxb069fP3t7+5MmTDx48aPC0nj17mpubE0KMjIz69OkTHR0dFRXl5+cne9fPzy86Orr+WqZ1y9k4Ojq+ugAAgPpiCtnvkukf3xBy9lCUELJ+0NcfdJ/CcQoSBCEhpHPnzumFpc9qpA2+G1dY0dmlmYN3ZXskEUIEAgHDMK84c8GCBRRFnTp16sGDB/Pnz5dIJE25Psuy9WOPoqjnjjS9AACAOhVS8k4IvcOT6+nz+hp6jZ+kAAhCMnToUCMjo+23GmiEhWYWxuYUTZkyRY63E4lEmpqaz83KSE5O9vPzMzU1ZVn20qVLL/ve2NjYwsJCQkhpaemtW7fc3d179+594cIF2bt//fWXu7u7QPDSv1MdHZ3KysqXbX8BACCz6AbtZc7FRkssYfMrChR9l0ahj5BoaWl9vyfozQkThBS1oLedroaIEEKz7B+pecuv3Zs/f567u7scb0dR1OjRo/38/GxtbVeuXCk7OGbMmLlz506aNCkiIuIVTTdra2s/P79BgwadP39+8uTJLi4uK1asGDJkSEFBga6u7h9//PHnn3++4tbt27fv0KGDt7e3kZHR3r17sUI3ALzoVCZzNZeNHa/wdJAw0i1/f1dc/XTz4JWKvterIQgJIWTs2LHHT5z4aNaHB+LDu5q31RAK7haWlddKvghYUpdVTXf48GEnJ6cNGzZYWlrKjgwbNqxbt24ODg7Hjh0jhBw/fjw5OTkvL8/CwuKrr77S09OzsrIaNGiQbMa9np5eRUWFhYXFi6Na7O3t9+zZc/ny5eHDh8s6IB0cHOLj40NDQ2tra1euXCnrQTx48KCzs3NgYKDsS0LIoEGDnJychEJhVFRUUlJSUVFRgxMNAaCVK6gicyKYE8OE+goeVF5WW/51+HpdDZ3AAUsVe6cmoJTnQdnBgweDg4MPHjzIwXc1qKqq6vz583fu3JFIJI6OjqNGjWrXrl3LLysvv/766+HDh8+dO8dvDRcuXPj11195rAEAFIQlZPRFaW9TamXPhkfRy0te+eOA0NW92vWY5z6zbg0THqFF+H9t2rSZMGHChAkT+C6kYRYWFj169OC7CgBQWzsSmYIq8lUPxaZgStG9ZWHr3nF5c0Kn0Qq9UdMhCFXG0KFDhw4dyncVAKCekp+ya+7QEX4isSKHyETmRG28sTPAc34/qz4KvM1r4m7U6L1796ZMmdK7d28PD49PPvmkpKSEs1sDAMAr1NDknav0pj4KX0TGWMto05AVSpWChMsgZBjG19d3//7927dvT0hIkK00BgAAvPsymu6oR81wUngidDJ26GTkoOi7vC7ugtDZ2XnKlCmurq59+/b95JNPbt26xdmtW6fExMSVK1c+e/bsgw8+4LsWAFBeYXnssXR23xuK7RpUZpxOqGcYJj09PSoqaseOHfKdpa5UCgsLzczMOLvdvn37Zs2a9eLx3Nzcc+fOMQwjm4MPAPCip7XkvTA6qL/QWFMh1y+sKv706vKiKqXuC+N0sEx5efnEiRMfP36sr6+/bdu2F0+4ePGira1t/SNjx45ds2bNK65ZXV2tPDNAZLKzs4uLi9PT0wkh1tbWGhoaGRkZOTk5NjY2HTp0IIQUFRUJBAKhUJiQkGBvb183SePhw4d5eXnu7u6FhYUGBgY6Ojo0TT948KCsrKxr166ampqyc6ytrTMzM4uKilxdXSmKysnJefz4cXp6ulgstrGxea4YfX393bt3v/iNdTsmPnz48PHjxy4uLrq6uk356aRSaXl5uZz+qACAZzMjxf5W7ADDakX8t8589mjl31uG2byhSYv5+tzQ1tZ+xXpbMpwGob6+fnR0NCHku+++GzFixIMHD4TC/zTG+/fvv3nz5vpH9PT0Xv0BraWlRSnBNJT6NmzYwDCMbK+JoKCgbdu2xcTEWFpaxsTE+Pr6fvfdd2vWrElLS8vPz2/Xrl1ERMThw4dHjBixdOnSQ4cO9e7dOy8vr7y8fPXq1X379h03bpyGhoaenl5aWtrp06ednZ1dXV3Hjh2blZVVWVlZVVV16NChw4cPl5aWzp4928bGRrbZRX1Pnjyxs7Orqal57hujoqIIIe+8805GRoatre3t27d/+umnIUOGNPrTiUSiJkYmACi5n+4xKc+YX4aI2iggCmLy4wJvbJnr/oG37SD5X12u+Jk+MWnSpPnz5xcVFT33CFFHR8fOzq7l1z/34HJ5bcWLx0c7+OiItWWvJbTk5L0GJqdrCMXjnEbVffm44kloVsSLp5nrmA5q79Xg3Xfs2PH7779fvnxZ9uXGjRtly7hUV1d37txZFpCZmZm3bt3S0tIKCgraunWrhYVFUFDQvXv3jI2NU1NTu3btSgj59NNPR44cuWLFCkLI3r17P//88zNnzhBCOnfufPDgQZZlPT09k5OT582bd+PGDdl2S6/WpUuXum88ffr0vXv3NDU1Y2NjKYq6fv36tGnTXrbrBQCon4wy9oso+rKvQlLw/IPgoDsHVw1Y0t3MRf5XlzfugjA+Pt7W1lZfX18qle7atatjx46K60grqXpaWlv24nGapeteM4QtrCp+8Rwt4X+elEsYSYOntRFpNbGYoqKiXbt2paSkVFRUlJWVyXaoHzFihOzhZI8ePbZs2RIZGTlw4EBjY2NCiLOzs4uLCyHk4sWLZmZmGzdulF2kbrfecePGEUIoiurevXtmZmaD29k3aOzYsfW/8dKlSzY2Nps2bZK9m5WVVVBQwGXvJgDwhWHJ9DD6yx7C7kZyfqLGEvan+COXMkJ2eK9vr28l34srCHdBGBYWNmDAAD09vadPn3br1u3kyZOKu9e7Xd9q9BxNocbcnu83epq1nmVTTnsFb2/v9957b/369ZqamlOnTq2uriaEaGv/0zAVCoU0TTMMU/8psUgkYlm2srLSxMTE0NCQEGJoaLh+/XrZu3XLhIpEIqm04d2jGvTcN5aXlxsaGsquTwjZtWtXXcchAKi3VbdpTSFZ2FX+4yUfPctNLEzZM2KrviY/eyo1A3dBOH/+/Dlz5jx58qRt27bq/YHbpk0bmqalUqlIJCouLk5LS/v8889FIlF5efndu3cb/BZ3d/c1a9ZUVlZqa2vn5OQkJSVRFOXm5mZmZtbgiNDnbldTU9OMOt3d3cVicaPXBwA1E5rH7r3LRI8VKWJ4RXt9q61DVivgwgrEaR+hUChUqmWsFURPT69bt27vvvuura3tokWLunTp8sEHH/Tr1+/o0aN6eg3/iuTh4TFixAhPT8+BAwdGR0d36NBBKBRu27Zt/Pjx9+7dc3JyysjIKCkp+eGHHxr83s8//3zx4sXW1taffvpp0+tctWrVgAEDysvLe/fu/fjx41u3bsn6IAFAjRVUkXdD6Z8Hiiy1lWuYIY+w1qhCXL9+PTQ0ND8/X0NDIyQk5Oeffy4oKNi+fXtOTo69vb2Dg4NY/M8eJx06dFi7di0h5Mcff7x582Zubu7KlSt79eplbW3t5uYWHR195syZnJwcOzu7ESNGEEK2b98u60okhLz99ts6OjouLi5RUVHR0dHPDRHu1q3bypUrDQwM9u/f3+A3WllZxcfH//777+np6aamprLOSABQYwxL3g2Vvu9EeVvJMwXjC5KM2hha61nK8ZpcwjZMyuLixYuOjo5aWlp79+49fPhwYmKiSKR0v6ZgGyYAlRYYywTnMFdHiYTyy8Hgh2HfxexbOSCgh1lXuV2UW0r3Udtqpaenr1mzpra2tkuXLhcuXFDCFAQAlRaWx36fQt8aI88UPJF65mjKH1uGrHIwlMPMN77g01ZZfPzxxx9//DHfVQCAenpSTd4NpQ+8IbLSkU8M0iy9/VZQUmHq7uGbTLVN5HJNviAIAQDUHMOSqaHS9xyp4dbyScFKSdXK65tYwu703qAtbiOXa/IIQQgAoOY2xDGltWRlT/nsL8Gw7OIry7qYdJrvPlNAcbpzg4IgCAEA1NnNAnZHEv33GLltPS+gqBX9P7fUVZ+5cOoQ5gAA0KDiGvJ2CB3UX9hBV57zJdQpBQmCEABAXbGEzAinJ3ak/DvI4aO+wZ0M1AOCEABAPW2OZ/Ir2cBeLe0aZFhmR/Te9Te+lUtVSkgd+gizsrJOnDjBdxWtwq1bt/guAQCaJOoJuzWB/ttfpNGy9k61tDowYmuVtHr1gCVyKk3pqHwQ+vv7X7t27ciRI3wX0lq88cYbfJcAAI0oqSGTr9J7+gtt9VrUNVhUVbI0LNCure2qAUtEAvkMOlVCKh+Ebdu23bt3L99VAAAoC5aQ98Pp8bbU2JZ1DWY8zQwIDfRz8JnadaK8alNOKh+EAABQ3zcJTE4le3Roiz7eY/LjAiO2zOn5gU/HQXKqS3khCAEA1MffBeymeDl0DVZKKlcPWOJq5iKnupQaghAAQE08qSaTrtJBLe4aJIQMsPGUS0kqAdMnAADUAf3vgqJj5DFrsFXBnxcAgDpYEkUzLFnR3AVFn9WUrbvxrRrPmn8FBCEAgMr74yHz+0P2t8HN3Gswtzx/7qUAXbGOtlhb3qWpAPQRAgCottSn7EcR9F/DRSZazfn25MK7y8LXvdd10lgnX3mXphoQhAAAKqxMQsYH05v6CHuaNKcxGJYV+U3U90s8F3pa9ZJ7baoCQQgAoKpYQqaH0cOtqWmOzennOpF65kjKH1uGrnI0tJN7bSoEQQgAoKpW3abzq9jDQ5rzSZ5alHYpI+SHEVtM2hjJvTDVgiAEAFBJl3LYfXfZqDHC5s2ddzZ2/GHEFvXYYr6F8EcAAKB6Hpax00KlRwYLLbWbP3ceKSiDPwUAABVTJSXjg+lV7sL+7V4vBe+XpD+rLVNQVaoLQQgAoGJmhNNdDalZzq/3AR6Zc+vTKyselDxUTFEqDH2EAACqZGsCc6+UjfB7vU/vs/cv7o//bc3AL7uZdlZQYaoLQQgAoDJC8tjN8fRNf1GbJn94s4T9Kf5I8MOwnd7rrfUsFVmdqkIQAgCohkcV7DtXpQcHiZq+uUQtXbv+xvYnlYW7h28y0NRXaHmqC32EAAAqoIYmbwbTn7sKfayamoJShl4Y/KVYKN42bC1S8BXQIgQAUAHzImlrHWpxt9dovYgEwjk9P+hq6kyRlm5PqN4QhAAAym5PKnOzgL05RvS6gYahMU2BIAQAUGoheezKGPqan0inaR/YUoYWCZq5K2HrhD5CAADllV7GTgmRHhosctBvvDXIEvbH+EMbb+7goDB1ghYhAICSeiYh/pfoFT2FQywbT0EJLdl4c2dOed66gcs4qE2dIAgBAJSRlCETgqUjrKnZTVhBpqy2fFn4en0N3W1D12iJNDkoT50gCAEAlNGCG7RYQDb2aby3L7c8PyBkdW8Lt3nuMwUUBoi+NgQhAIDS2Z7IhOWxkf4iYWO5llx4b1n42qldJ45zGsVJaWoIQQgAoFwuZrMb4ugIf5GBRuMnJxfeDfBY0NfSXfF1qS0EIQCAEkl5yk4Pk570Ftk1bR21N539FF2S2sP0CQAAZVFUQ/wv0Zv7Cj3N0NXHHQQhAIBSkDDkzWDpZHvqXYdXfTJXSqr2xv0iYaScFab2uHs0Wlxc/PPPP0dERFRXV3t4eCxatEhXV5ezuwMAKLm5kbSRJrWq56uGiRZWFS8NDXQyssfyoXLEXRBGR0ffvn170qRJOjo6GzZsuHHjxrlz5zi7OwCAMtsQx8QUsuGjRYKXB1z608wloatH2g2b4fo2h6WpP+6C0MfHx8fHR/ba1ta2W7duVVVVbdq04awAAADldP4RuyuZueEvfMVqorfyYtdGfjO/16yhHQZwWFqrwM+o0bS0NDMzM6QgAMCdInZ6mPTscJG1zksbg2fvX9offyjwjaXdTLtwWVsrwUMQFhUVLVy4cP369S++FRoa2rt37/pHhg8fHhAQwFVpAACcelxN+V3W2NhD0lmruqys4XPiniQdTvp9k9fydlpmZS87CV5CW1tbKGxkdR6ug/Dp06fDhw+fPHny9OnTX3zX1dV12bL/LBdramqqp6fHUXEAAByqpsnUEOnHXQQzur5q5nx/PQ/39j3aiLQ4K6y14TQIy8rKfH19+/fvv2HDhgZPMDIy8vDw4LIkAABe0Cx5N5R20KeW9mh8GhtSUKG4m0dYWVnp5+fXpUuXbdu2cXZTAADl9MlNuria3Teg4cVEc8ryMFOQM9wF4Z9//hkWFvb7778bGxsbGRkZGRk9fPiQs7sDACiPlbfp0Dz2pLdIs6HeqzuPE+ZeCkguvMt5Xa0Ud49G33zzzZEjR9Y/YmBgwNndAQCUxJ5U5tf77HU/UduGegavZl7bGbNvRf/Pu5u5cF5aK8VdEGpoaGhoNGEpdQAA9XU6k1l1mw4bJWr3wvQxlrA/xR+5mHH126FrOhjY8FFdK4XdJwAAOBKax354nb4wQuRo8HzPoISRbv77u6zS7O+HbzbUastLea0WghAAgAsJxeykq9JfB4ncjJ9PwWppTUDoan0N3W+HrdUSafJSXmuGIAQAULiMMnbkRfq7fkJvqwZGiWqJNMc6jhzY3ktAYSltHiAIAQAU60k1GXmB/sJV8FbHlw7UH9yhP5clQX3YjxAAQIHKJGTkBenb9oIFLvi8VVL4iwEAUPgFM34AACAASURBVBQJQ966Iu1lQq3o+fyH7dGUP3fd/pGXquA5CEIAAIVgWDI1lNYSUru8hP89znx7a89f6Vfe7OTHV21QH/oIAQAU4tO/6cdV7F8jRPVXUauSVq++vrmWkezy2agj1uavOvg/BCEAgPytiWWu5LLho0Va9VqDhVXFX4ausTe0/bTPXJGgkb2BgDMIQgAAOTuYxvyUxlwb/Z9F1NKfZi4JDRxpN3SG69v8lQYNQBACAMjTmSwmIIoOHS2y+O+Dz4vpV+f0nDGovRdPdcFLIQgBAOTmZgE76xp9drio0wuLqH3ccwYvJUGjEIQAAPKRWMKOvSw9OEjkboIFYlQJpk8AAMhBdgU7+iK9w1Po8+8iajV07am0v1jC8lsYNApBCADQUoXVxPsvelFXwUS7fz5Un9aULg5eFl+QTDMMv7VBoxCEAAAtUikl/pekb3WkFnX95xM1pyxv3qUlzsaOX/X7BNMklB/6CAEAmk/CkAnB0q5G1Gr3fwIv8Unq19fWz+j2tr/jCH5rgyZCEAIANBNLyIfXaLGA2t3vnxQMzYrYFvXDl/0W9bV057c2aDoEIQBAM332N323lL3iKxIJCCEkMifq+9sHvvVe29GgPd+lwWtAEAIANMeGOOZSNhs+WqT97+doHwv3H0ZsNdQy4LUueG0IQgCA17bvLhOUylz3Expq/v+gSCBECqoijBoFAHg9++4ygbHMxRFCS22qpLoUMwVVHYIQAOA17LvLrIllrvgKHQ2o1KK0mecXphal8V0UtAgejQIANNXeVGbtHeaKr9Ben7r26OaWv3d94TG/s7ET33VBiyAIAQCaZE8qsyGOuTpKaKdHHUs9dSzl1KYhKzoZOfBdF7QUghAAoHE/pDAb45mrvsIOuuz26KDYx4m7fDaa65jyXRfIAYIQAKAR2xKZHUnMVV+hRZuar8I21zKSXT4bdcTajX8nqAIEIQDAq2xNYPakMtdGC611KCkjdmvnOt5pNFYQVScIQgCAl9qSwOxNZUJ8hVY6FCFEJBBOdB7Dd1EgZwhCAICGbYpnfrzLhIwSWmpjo111hnmEAAAN2BjH/HiXuTpKeDv30rGUP/kuBxQIQQgA8LyNccxPaczVUcKL948cSvrdw6o33xWBAuHRKADAf6yIoY9nsJdHsPtjv8krf/z9iM1tNbGCqDpDixAA4P+Wx9CnMtlzw6s23lguZaTbhq1BCqo9tAgBAP6xLJo+94g9NLBweeiq3hY957nPFFAYJqP+EIQAAIQQ8lU0/dcjNthXtCv618ldxo+y9+a7IuAIghAAgCy9RV/MZi/7iow1ydden1IEDcFWBEEIAK0aS8jim/S1fDbYV2SkSQghSMHWBoNlAKD1YglZdIO+ni9d3+OOkWbj54NaQhACQCvFErIgko4prOinuyY08wLDYqP5VgqPRgGgNWIJmR9Jxz0pdBCtb6/nuLjPRxgg2mohCAGg1WEJmRdJxz/JMKfXDezoPcP1bb4rAj4hCAGgdWFYMvMa/aDotjH73aI+c/pb9+W7IuBZU/sIT548WVVV1ZI7sSwbHR29Z8+eJUuWZGVlteRSAADNQ7Pk/XD6QVGkMbt7w8BlSEEgTQ/COXPmWFhYzJ49Oz4+vnl3oml68uTJISEh3377bU5OTvMuAgDQbLIUfFjOHvVx+374RmdjR74rAqXQ1CAMCQn56KOPTpw40b179169egUFBVVWVr7WnUQi0f37948cOdKmTZvXrxMAoEVolswIo/Mr2b+Gi9rp6JrrmPFdESiLpgZh586dN2zYkJOTc+zYMUNDw9mzZ1tZWc2ePTshIUGh9QEAtBzNkmmhVQXV7J/eojYYGgH/9Xr/IrS0tN5666233norPj5++/btQUFBe/fuHThw4OLFi/38/KgWDz6OjIz09fWtf2TQoEFz5sxp4WUBoDWrpsmMa3llZRu+HfAFXW1Vznc9wCVtbW2BoJEmX3N+NUpMTNy3b9/JkydFItGoUaNyc3PHjBkzcuTI06dPi0Qt+l3Lzs5u9uzZ9Y/Y2Nhoa2u35JoA0JoV15DxwXdEVdsC+sx0tUSnYKvTaAqS1wrCqqqqY8eOBQUFRUZGWlpaLliwYNasWVZWVoSQ8+fP+/v7BwcHjxgxovn1EtKuXbsxY8a05AoAAHUyytgJ5y8bsr9uHhLQ07wr3+WAkmpqEAYEBAQFBZWWlg4ZMuT48eNjxowRi8V17/r6+trb22MsKAAoj7hi5r0Lh63EYT8MX9de35rvckB5NTUIT58+PX369I8++qhTp04NnrBjxw4nJ6dXX8Tb2zs9Pf3Zs2dvvvmmlpZWaGiojY3N69ULANAEfz2qXRq2o5P+4z0+mw21sMU8vEpTgzAuLk5DQ+MVJwwfPrzRi/z4448SiaTuy3bt2jXx7gAATffjPWbZrYr3bY2Xey7QEL7qgwuAND0IX52CTYT2HwAoFEvIqtv0r/fZ0NFtnQxm8F0OqAZMqAEANVHLkA/C6bRnbKSfyAzrdkCTIQgBQB2US8j482FiAXXV9w1tfLDB68DGvACg8nIr2aF/nGKqf/7GyxopCK8L/2QAQLUlFNPTLvxgoZF6wHeTmbYJ3+WA6kEQAoAKu/Co6qvwTV0M6D3DN+qIsQoVNAeCEABUyaNHj2JjY01MTPr06bMv7emB24EDLR03D/pYSAn5Lg1UFYIQAFTG8oDPrp4+2c9c90kNPaOYNVg6cqrroPk9x/FdF6g2BCEAqIYLf/2VEnzm8HAn2TY3cQXPNu+LnH99K89lgerDqFEAUA3n/zjxjr1h3WZv3c30awsfv+4O4QAvQhACgGqgpVKBgMrQ+f++pwIBxTAMjyWBekAQAoBqcB4y8rvO2sethCxFCCFpxRVCHQNdXV2+6wKVhz5CAFABV3JKf6Vu62gYpu1L+MVIo0hCruZV/nbqLN91gTpAEAKAstuXnPljbOCwDkPWTNmYMCohJjq6q4nJGm/vNm2woijIAYIQAJTashtxoelbZrjO+LDbEEKIq6urq6sr30WBWkEQAoCSYgmZdfV6an7Qcq/PfWwRfqAoCEIAUEY1NJkWRhdUdPxh+DoXY2u+ywF1hiAEAKWTV0kmBEs76lEXRllpYGw7KBj+iQGAcgnLY3qfko60Efw6WIgUBA7gXxkAKJFv4nIDri7e2qfoazcB1fjpAHKAR6MAoBTKJeS9K6mFxetndntrkr053+VAK4IgBAD+pZWyky9FGEj3rOq/YHD73nyXA60LghAAeHYmi/ni2ukO4tM7hq90MrLnuxxodRCEAMAbmiWBsZLTqftcdZN3DNtormPKd0XQGiEIAYAfhdXknRCphC7yta760nOTthjrpQE/EIQAwIOYQvatK/REO2ptr3ZC6hO+y4FWDUEIAFwLSmW+iqb39BeOt8UMLuAfghAAuFNNk3mR9K286ANe+qNtO/NdDgAhmFAPAJzJKmffOCstfHbBTrTbTg8fPqAs8G8RALhw/hHb+5TEVfuYNn16p/f6Liad+K4I4B94NAoAisUSsimO2Z1cPcl8F8082Tp8s4GmPt9FAfwfghAAFKi4hkwJkVZIyoYbbjTSMvrSc42GUIPvogD+A0EIAIpyp4idEEwPsyKkfK2Hpft018kUwUraoHQQhACgEL/cZz77m97pKZxoJ3hWs0JfU4/vigAahiAEADmrockXUfSFbPaqr8jFkCKEIAVBmWHUKADIU3YFO+ic9GE5e867RJaCAEoOQQgAchOax/Y9Rfu3Z/ro7Nx/5we+ywFoEgQhAMgBS8j2ROadEOker6r8wlVV0uoV/b/guyiAJkEfIQC0VGktmRZGP6lmzw0r2hYV2Ktdj3nuMwUUnouCakCLEABaJCyP7fGHtL0u2d03fc31JWMdfRf0+hApCCoELUIAaCYJQ9beoYNSmT39hYaCW8vDv1viudDTqhffdQG8HgQhADRHUgk7NZS206fix4tNtEhSocGWoascDe34rgvgtSEIAeD1sITsSGTW3qHX9BLOcv6ne8XFxJnfqgCaDUEIAK8hs5ydHkbXMuSGv8heHx2BoA44HSyTnZ0dGBj4+eef37hxg8v7AoBcHM9gPE5JR1gLro0WGYiKP7u6oqS6lO+iAFqKuyAsKirq3bt3QUGBhYWFr6/vpUuXOLs1ALTQk2oyPphefZv5a4QooLvgYWnmnEsBLibOhloGfJcG0FLcPRrdv3+/m5vbzp07CSFisXjDhg0+Pj6c3R0Amu1iNjvzGj3eljo8WKQpJNF5d9ZEbp3nPnOY7UC+SwOQA+6CMDw83NvbW/ba29v7k08+YRhGIMBERgDlVSUlS27Rp7PYXwcJB1pQhJBzDy7vvfPL6gFLXM1c+K4OQD64C8L8/HxTU1PZazMzM6lU+uTJE3Nz8/rnxMTETJ8+vf4RT0/PadOmcVYkANS5VUi9HylwbcveGMm01ZBWVbO/Jp+4+ujaljdWWutZVldX810gQOM0NDQabXFxF4RisVgqlcpey15oaDy/UbWxsbGXl1f9I05OTmKxmJsKAUBGypBvEtnvUshOTzKmvYAQISHk4bNHKSX3dvts0tfAnkqgMqgmLHLEXRBaWlrm5OTIXmdnZ7dp06Zt27bPnWNra/vhhx9yVhIAvCjlKTs1lDbVIrfGCi21//8hYm9o+83QQB4LA1AQ7rro/Pz8/vjjD1lb8Pjx4/7+/k0JagDgDEtIUCrzxlnpVAfB+RGi+ikIoMa4axFOnjx5z549AwcOtLGxuXr1akhICGe3BoBG5VeRD8KlxTUk0k/kaPBPBMYVJJlqG1vqtuO3NgCF4q5FqKWlFR4evnz58jfffDM1NdXFBUPOAJTF8Qymx0lJb1Pqer0UvPwwdMW1DU8qi/itDUDROF1iTSwWDx8+nMs7AsCrldaSeZH07UL2/HBRT5P/Pws9kXrmaMofW4ascsA62qDusNYoQOsVnMO+H06PtKFujRVp//thQLP0t7f2JBfe/X74ZhNtY14LBOACghCgNSquIQFR9OUc9qeBwiGW/28IVkqqVlzfqCnU2OWzSUukyWOFAJzBwi4Arc7xDMblhERAkfgJovopyLDMwuAvO+hbrx6wBCkIrQdahACtyP1n7JwI+kk1+dNb1Nfs+dkRAkqwov/n1nqWvNQGwBe0CAFaBQlDNsYxfU9Jh1oKosc2kIIySEFohdAiBFB/YXnsxxG0vT65M15ko/N8BFZIKnXE2rwUBqAMEIQA6uxxFfn8bzokj93uKRhv+/wTIIZldsbsLa56umpAAC/lASgDBCGAemIJ+SWNCYiiJ9oJUt4U6b6wdn2VtHr19c21jGT1gCV8FAigLBCEAGoovpj96DotoMhlX1FXwwa6AwuripeGBjoa2n3SZ45IIOS+QgDlgSAEUCuVUrIpnv4+hfmyu3C+i0DQ0JiYjKeZS0IDR9gNneH6NucFAigdBCGA+jibxc6LpPuYUgnjxWZtGj4nJj8uMGLLXPcPvG0HcVocgLJCEAKog9xKdkkUc6OA3TtA6G31qu2TymrLA99Y2s20C2e1ASg5BCGAapMyZFcyExhLz3QWJE4QaTbW3zeovRcndQGoDAQhgAq7Xch+FEFri8h1P5FzW+yjC9AcWFkGQCWV1pKFN2i/S/S8LoKQUa9KwdKaZxtubK+UVHFZHoAKQRACqJ4zWYzrSWlJDYmfIHrPscGRof/ILc+fdylAW6ytJdLirj4AlYJHowCqJOUpu/gmnV9Jjg4RerxkvdA6SYWpX4evn9Zt8hjHkdyUB6CKEIQAqqGgiqy8Tf/+kFnaXTivi0DU2NOc0KyIbVE/LO230MOyFycFAqgqBCGAsquSkh1JzJYEerytIHGC2LQJzzhPpJ45mvLH1qGrHAztFF8ggGpDEAIoL5aQExnMF1FMV0Nyw1/koN+kcaFJhamXHob8MGKrcRtDRVcIoAYQhABKKiSP/exvWkSRgwOFA9q9xtQIFxPn74dvFlJYQRSgSRCEAErnbin7dTTz9xM20F0w9ZWDQl8GKQjQdJg+AaBEimrIwhv0gDNSdxPq7luNTI2o735JenlthWKLA1BTCEIApVAlJRvjGOfjkmqaJL0pDugu0Gpyoy4yJ+rTKyvuP81QZIEAaguPRgF41rwRMXXO3L/4c8LRjYOXOxs7KqhCAPWGIATgU7NHxBBCGJbZe+eXyJyo73w2tNMxU1CFAGoPQQjAjxaOiKmWVgdGbK2UVu3y2aSroaOQEgFaB/QRAnCt2SNi6kgY6cLgr/Q0dDcPXoUUBGghtAgBuFN/jZikN5u0RkyDxALR3J7vu5q5yLU6gFYKQQjAhWqa7E1lNsUznmbUTX+R/WuOiHkRUhBAXhCEAIpVy5Cf7jGrY5nObcnJYcLeps2PQClDiwSYKQ8gZwhCAEWpocnPaUxgLNPDmPzpLexl0vwIZAm7P+5QUVVxgMcCOVYIAARBCKAIFVKyL5XZnMC4GZM/vYXuLYhAQoiElmz6e2d2Wd66gcvkVSEA1EEQAsiTLAI3xTM9Tchpb2HPlkUgIeRZbdnXYesNtPS/HbZWU6ghlyIBoD4EIYB81I/As8OFbsYtjUBCSG55fkDI6t4WbvPcZwooOVwQAF6EIARoqXIJ2X+X2RhPu5tQ54YLe8gjAgkhyYV3l4Wve6/rpLFOvnK5IAA0CEEI0Hx1EdjfXHDVV+TcVp6NtoQnKUs8Fvax7CnHawLAixCEAM1RJiG7k5ktCfRgC/lHoMykzmPlfk0AeBGCEOD1yCJwczw9xFJw3U/UyQBddwCqDWuNAjTVMwnZGMfYH5UklbCR/qJjQ4XyTcEKSeX+uENShpbjNQGgUWgRAjSuqIbsTKJ3JzMjrAURfiJHBbQCC6uKl4Ss7mTsgMGhABxDEAK8SmE1+SaBDkplJnQURI0R2eopJKYePH24NDRwpN2wGa5vK+L6APAKCEKAhiWVsDuSmOMZzCQ7we1xova6imqpReXdXhuxbWHvWUM6DFDQLQDgFTgNwoqKitjY2Ly8vCFDhhgbG3N5a4AmYlhyNZfdnkRHP2GnOQkSJ4gstRX4sPLs/Yv7439bM/DLbqadFXcXAHgF7oJQKpUaGRk5OjrevXs3PDzc09OTs1sDNEW5hPz2gNmeyGiJyGxnwfGhAi0F7/QQlXf7WOrp3T6bLHTNFXsnAHg57oJQKBQWFxfr6OgYGhpydlOApsgoY/ekMvvvMh5m1HZP4TArjsar9LZw2zNiaxtRc/fnBQB54C4IKYrS0dHh7HYATXE9n92RxFzNZaY4CKLHijoorCOwQRShkIIAvFOuwTKJiYlffPFF/SNubm7jx4/nqx5QVzU0OZtNvk2mntZSs53YHzxYHRFDCKmpUfit8yoem7Yxwf66ANzQ0NCgGpuTpNggjIuLCw8PJ4TY29v7+ja+cLBYLNbX169/RFtbWyDArH+Qm8dV5OB9sjuVOLclX3YnvtaEIhQhHDUEYx8nrPv72xX9Pu9q4szNHQGgUYoNwoqKiry8PEKIkZFRU87v1KnTsmXYehQU4nYhuyeVOfmQGW8ruOQr6KKA1UFf7UL61R9if1rZ//Me5t04vjUAvIJig7Bfv379+vVT6C0AXo1hyblHzI4k5sEzMttZcPctsZEm1zWwhP0p/siljJDtw9Z2MLDh+vYA8Eqc9hEuWrQoNze3oqJi2bJlxsbGO3fuNDfHqHFQlNJa8tM9ZlsiY61DFnYVjOsgEPHxlF3CSDfd3JldlrN7+CZDrbY8VAAAr8RpEE6cOLGysnLWrFmyL5/rDgSQl7RS9rtk5pf7zDBLwdEhwr5mvC3fWS2tDghZbaCl/+2wdZpCDb7KAIBX4DQI8ZgUFIrjRWGaQlOk6e80cnD7/gKspQ2grJRr+gRA8xTXkF/vM98lM201yEIXwe/DBBrKMdaYItRQrCAKoNwQhKDCaJZcymYP3GMu5zC+NoKf3hD2M0fDCwBeD4IQVFJWOXv4AftDKmOsSaY6CL7vLzbmfCzoyxxOPvmspmy22zS+CwGAJkEQgiqppsmZLCYolbldyL7ZUfDHMGEPYyVqAjIssyN6b1xB4oZBy/muBQCaCkEIqiGmkA1KZY6mM71NqVnOgjEdlKUXsE6VtHrV9U1Shv7OZ6OOWJvvcgCgqRCEoNTyKsmxdGb/PaaWJpPtqfjxCtwgtyUKq4qXhgY6Gdkv7v0x1hEFUC0IQlBGtQy5mM38ksZeyWVG2Qi+6SscaqW88w/Sn2YuCV090m7YDNe3+a4FAF4bghCUS/JT9mAac+AeY6NDzXIW/PiGWFfMd02NOffg0tyeHwxsj2myACoJQQhK4WktOZbOHExjHpaTdx2oSD+Rvb7StgCfN9/9Q75LAIDmQxACn2RrwRxMY84+YoZZCgK6C3xtBEKVSUAAUAcIQuABS0hUAXssgzmWzlpokxlOgh39xG1VZyXOGrr2UkaIn8NwvgsBADlAEAKnogvZY+nM8QxWW0gm2gkujRR05nxfwBYqqS79MmyNtZ6Fr/0wIYUBogAqD0EIXEgqYY9nMIcfsLUM8W9P/TJQ2L+diuWfTE5Z3hchq/paus/vNZPial97AFAoBCEokCz/jqazVVIypgO1f4Cq5p9MwpOU5dc2vO/6Dh6KAqgTBCHIX/JT9lg6cyydrZCSsR2ovf2FXu2UdxZgE4VkXt8Zs3e512du5t34rgUA5AlBCHKTUcaezmSPZzBZ5WScLRWkFvknc+3RjT13fv5m6BpbAxu+awEAOUMQQktllrN/PmSPZzCZ5WS8LbWht/rkXx0Py15dTbsYahnwXQgAyB+CEJopq5z94yF7PIO5W8qOtFbzKYBiodhQiBQEUE8IQngNDEtuPWHPPmLOZrF5leyEjoK1vYQD2lECdcy/pzWlbTURfgDqD0EIjauUkiu5zNks9mwWqyUko9tTm/sIB1pQYiXbCEmOkgvvfR2+bv2gr52M7PmuBQAUC0EIL/WwjL2Uw57JYkJy2R7GlF97wRVfgbOqzX9vhmuPbmz5e3eA53ykIEBrgCCE/2BYElvEnslizmaxmeXsYAvBWx0Fvw4SGKjO+mctdCL1zOGUk5uGrOhk5MB3LQDABQQhEEJIhZRczWXOZrGnMxkjTcqvA7Wht3CQBSVS34efL2JYZkf03jsFibt9NpnrmPJdDgBwBEHYqmWUsZdz2DNZTHge28eMGm0j+KqHkm4Br2hV0uqV1zYxLLPLZ6OOWJvvcgCAOwjCVodmyZ1/H35mlbMjrAXvOQp+GyzQU/r9bxVKRAl7tnN909kP62gDtDYIwtYiv4pcyWHOPmIvZTMd9ajR7ak9/YU9TdRt5nuziYXiSZ3H8l0FAPAAQajOnklIWB5zJZe9ksPmVLKDLAQjramtfUWW2og/AIB/IAjVjZQhccVscA4bnMvcesJ2NaT6t6O2eaj5tL/mOZ12QcJIJnTy47sQAOATglAdyOY8XM9nIx6zl3MYe31qmBUV4Crs347SQodXQ1jC/hR/5PLD0I2DlvNdCwDwDEGowtLL2OAcNjiHvZLLtNWghllRb9lRe/qLDTX5rky5SWjJ+pvb88sLdg/fhEXUAABBqGIeV5HwfCY4h72YzdbQ7IB2gmFW1FYPkY0Ouv2a5FlN2Vfh64y02m4btkZT2GqWCQCAl0MQqoCiGnItn7mSw17JZQuq2EGWgqGW1KfdBE4GCL/Xk1OWFxC6uo9Fz3nuMwUYMAsAhBAEoXJiCbn7lI0sYCPy2cgCNreC9TSnhlgKfhkkcDNWz60euBF05+CULhNG2g/juxAAUCIIQmUhYUh88T8DXkLzGJGA9DcXeJlTM5wEfc0w4FM+Vg74giL4PQIA/gNByKfHVSTqCRNTyEY8Zm88ZjvoUv3bUaPbU5v6iGz18Hktf0hBAHgRgpBr6WX/NPuu57PZFWwfM8rLnFrgIjgxtBXt8MAZCSO9nR/X19Kd70IAQHkhCBWuQkpiC9mIx+z1x8yNx6yG8J9nnrOc0eGnWOW1FV9fW68j1ulj2RNtQQB4GQShQuRWsrIHntfz2TtFrHNbysuces9RsH+AwKwN38W1DvkVBQEhq9zb9Zjn/gFSEABeAUEoH+ll7J0iNq6IvVNMbheyEob1NBP0b0dt6iNwN6E0sbwLt1KL0r4KW/uOywQsnwYAjUIQNkcNTZJK2DvFbFwRe6eIjStm9cVUD2OqhzF5z4Ha5iGww1AX/lx7dHPL37u+8JjvZd2H71oAQAUgCJuktJYkFLMxhWzyUzaphL1TxHbQpVwMqS6G5DNXQR9TgTkeeCqHkMzr393ev2nIik5GDnzXAgCqAUHYMFknX0whm1xCkkrY7Aq2mxHlYkh1aUtNdRC4m1Bt8CenlNzbdd/ts8lcx5TvQgBAZeDjnBBCJAy5V/pv8j1l7xSxYgGRxd7o9tSKnoLObTG8UzXoa+rpa+rxXQUAqBJOgzA7O/vGjRtVVVUeHh5OTk5c3vo5T2tJ4ksedS5wEfQ1xdhOVVJD12L5bABoNu6CMDg4eNKkSYMHD9bR0Vm4cOHXX3/9ySefcHb35x515lSyXQ3xqFMdpD/NXBoauHnIqvb6VnzXAgAqibuP/x49emRmZurq6hJCLl68OH78+AULFohECinguUedsYWshpC4m1AuhnjUqVZi8uMCI7bMdf8AKQgAzcZdEJqYmNS9NjMzo2maYRh5XTy3kk0uIbFFbFwxe6eITS9jOxlQ3Y2oHsbUWFtBDyMKe9Wqn/MPgoPuHFw1YEl3Mxe+awEAFcbDA0GWZVetWjVt2jQNjef7de7fv79ly5b6R7p06eLt7d3gdc5nk1NZJPkpuVtKNIWkswHpZkQGm5NFnUnntkRDwBLC1p0skcj95wDesIT9Jen45Yeh3wwOtNGzlOBvFwBeQiQSUY1tPqrYIHz06FFkZCQhxMTEZOjQobKDX375ZXZ29sGDB188zH3oQAAACOZJREFUv6KiIjMzs/4RWduxwYuLCdXLiEy1I84GxFCD/c97LHnJN4HKk9CSrTHf51cUbB+y1kBD/2X/PAAACCFCoZDnIMzPz798+TIhxN7eXhaEq1atOnfu3NWrV/X19V88v3v37jt37mzixX07yrFSUBm1NRIzXZMvvRZpYKQoAMiDYoOwd+/evXv3rvty69athw8fDg0Nrd9fCPBa9DX15vR8n+8qAEB9cNdHePHixc8++8zPz2/FihWyI2vXrkUiAgAAv7gLQnt7+z179tQ/8uJgGYAGXXkYriEUD7Dx5LsQAFBD3AWhg4ODg4Pc1kGWSqVnz54dO3asvC4ISutE6pkjKX9sGLSs/sEzZ874+PhoamJaTGsUEhLi6upqbGzMdyHAg1u3bpmZmXXo0EGO1xTI8VpcqqysfO+99/iuAhSLZulvor4//+Dy98M3ORja1X9r5syZT58+5asw4NeyZctSU1P5rgL4sWvXrpCQEPleEwuLgZKqlFStvL6JZdmdPht0xNp8lwMAagtBCMqosLIoIDSws7Hj4j4fCSkh3+UAgDqjWJZt/CxOnD9/ftmyZZaWlk05mabpW7dueXh4KLoq4EW1p0BQxGrce+k/zqioKDc3N7FYzGVVoCTi4+NtbW0bnIsMai8tLc3AwMDMzKyJ5+/cubNjx0ZmnStREBJCQkJCKioq+K4CAADUxBtvvNHo70zKFYQAAAAcU9VRowAAAHKBIAQAgFZNZUaN/vXXX2fOnNHX1//444+fm0qZlJS0f/9+iUTy9ttv9+vXj68KQXFSUlL27dtXW1s7ceLEAQMG1B0vKirat29f3ZdDhw7t1asXHwWCopSXl0dHR8fFxRkbG7/77rvPvRsZGXn48GGxWPzBBx+4uGBbSnVD0/SdO3diYmJKSko++eST+oPjMjIyjh07Vvfl+PHjHR0dm30j1WgRHj9+fPr06W5ublKp1MPDo6SkpO6tBw8e9OvXz9jY2MnJaeTIkRERETzWCYqQlZXVr18/fX19Z2dnf3//0NDQureePHmyevXqkn/V1NTwVyYoxN69excvXnzkyJHvv//+ubciIiJGjhzp5ORkbGzs5eX14MEDXioExYmPj580adKpU6eWLFlSW1tb/627d+9u37697v9+SzclZVWBu7v7gQMHZK+9vb23bdtW99aiRYvef/992evAwMBx48ZxXx4oVEBAwJQpU2SvN23a5OvrW/dWSkqKmZkZT3UBd/bv39+vX7/nDo4dO3b16tWy1x988MHixYs5rwu4INuktry8vP7Bv/76q0+fPvK6hQq0CKuqqmJiYoYMGSL7csiQIfWbfRERES97C9TDq/+Kq6qqVq1atWnTptjYWD6qA95ERkYOHjxY9hr/91uhgoKCr7/++ptvvrl//34LL6UCQZifn08IqduwydTUNDc3t/67dWvvmpqaFhYWtrSNDEomPz+//t9+aWlpZWWl7EtNTU1/f38NDY3s7OyBAwceOHCAvzKBU1KptLCw8GUfC6D29PT0hg4dqqurm5SU5ObmdunSpZZcTQUGy2hpaRFC6uKttra2TZs2de9qamrWf0skEolEKvBDQdNpamrWdQ/U1tYKBIK6PvOOHTv++uuvsteenp6LFy+eMWMGP1UCt4RCoUgketnHAqg9Ly8vLy8v2WsHB4fly5f7+Pg0+2oq0CI0MzMTi8XZ2dmyLx89elR/GTYrK6vn3qIoiocqQWGe+ys2NzdvcGW1Xr16FRQUYLxMK0FRlIWFRf1/GFZWVvyWBHzp1avXo0ePWnIFFQhCoVDo5+f322+/EUKqq6v/+OOPcePGEUIuXLjw+PHjsWPHHj16lGEYQsjhw4exQ6H6GTt27LFjx2iaJvX+imNiYhITE0tLS+tOO3r0qLOzM3YoVHtSqfTUqVNlZWXjxo07fPgwIYRhmKNHj+L/fitx7dq19PT0uv/7LMseP368e/fuLbmmaiyxlpiYOGzYsL59+z58+NDS0vLMmTMikcjExOSnn34aOHDg4MGDNTQ09PT00tLSrl27hl8M1UxlZeWQIUNYljUyMkpJSQkPD2/fvv3kyZPNzc319PR+//33Tp06ZWdn5+bmHjt2rH///nzXC/J0/fr1RYsWFRYWFhUVderUafDgwcuXL9fX109ISDA0NBwwYICjo2NZWZlEIrl69aqenh7f9YI8SSQST0/P2trahIQENzc3XV3d8PBwDw+PSZMmxcTEJCcnd+jQ4e7duxKJ5MyZM87Ozs2+kWoEISGktLQ0IiLC0NCwb9++AoGAEHLv3j1LS0tdXV2JRBIREVFbWztgwAD0E6glqVQaERFRXV09YMAAbW1tQkhOTo5IJDI2No6Pj8/OzjYxMXFzc8PfvvqprKyUDZeT0dHRMTU1TU1Ntbe319TUrKqqCg8P19TU9PLywlYk6odl2YyMjLovBQKBra3tw4cP9fX1dXR0YmNjCwoK2rVr1/KNaFQmCAEAABRBBfoIAQAAFAdBCAAArRqCEAAAWjUEIQAAtGoIQgAAaNUQhAAA0KohCAEAoFVDEAIAQKuGIAQAgFYNQQigGnJzc+3s7KZOnVp3JCIiwsTEZMuWLTxWBaAGsMQagMo4c+bMmDFjfvjhh1mzZpWUlPTs2dPGxubq1avYgxOgJRCEAKpk/vz5+/bti4yMXLVq1bVr12JjY9u3b893UQCqDUEIoEpqamr69et3//79srKys2fP+vr68l0RgMpDHyGAKtHU1Jw1a9azZ888PDyQggBygRYhgCrJzMx0c3OztrZOSEg4cODA9OnT+a4IQOWhRQigMqRS6ZQpU/T09EJDQ2fOnDlv3rzk5GS+iwJQeWgRAqiMgICAbdu2hYWFeXp6VldXe3h4SKXSqKgobW1tvksDUGFoEQKohgsXLmzZsmXjxo2enp6EEC0trd9++y0jI2Px4sV8lwag2tAiBACAVg0tQgAAaNUQhAAA0KohCAEAoFVDEML/2qsDAQAAAABB/taDXBIBrIkQgDURArAmQgDWRAjAmggBWBMhAGsBEGPjdmLDycgAAAAASUVORK5CYII=",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=3}"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dfdx = x -> exp(x)*(x+1)\n",
"slope1 = dfdx(x1)\n",
"tangent1 = x -> f1 + slope1*(x-x1)\n",
"\n",
"plot!(tangent1,0,1.5,l=:dash,label=\"tangent line\",ylim=[-2,4])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In lieu of finding the root of $f$ itself, we settle for finding the root of the tangent line approximation, which is trivial. Call this $x_2$, our next approximation to the root."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x2 = x1 - f1 / slope1 = 0.8678794411714423\n"
]
},
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=4}"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"@show x2 = x1 - f1/slope1\n",
"scatter!([x2],[0],label=\"tangent root\")"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.06716266657572145"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f2 = f(x2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The residual (value of $f$) is smaller than before, but not zero. So we repeat the process with a new tangent line based on the latest point on the curve."
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"x3 = x2 - f2 / slope2 = 0.8527833734164099\n"
]
},
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"\n",
"\n"
],
"text/plain": [
"Plot{Plots.GRBackend() n=4}"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plot(f,0.8,0.9,label=\"function\",\n",
" xlabel=\"x\", ylabel=\"y\", title=\"Second iteration\", legend=:topleft)\n",
"\n",
"scatter!([x2],[f2],label=\"starting point\")\n",
"\n",
"slope2 = dfdx(x2)\n",
"tangent2 = x -> f2 + slope2*(x-x2)\n",
"plot!(tangent2,0.8,0.9,l=:dash,label=\"tangent line\")\n",
"\n",
"@show x3 = x2 - f2/slope2\n",
"scatter!([x3],[0],label=\"tangent root\")"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.0007730906446230534"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"f3 = f(x3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We appear to be getting closer to the true root each time."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia (faststart)",
"language": "julia",
"name": "julia-fast"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "1.4.1"
}
},
"nbformat": 4,
"nbformat_minor": 4
}