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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"\n",
"import matplotlib.pyplot as plt\n",
"from IPython.display import HTML\n",
"import numpy as np\n",
"import random\n",
"\n",
"def hide_toggle(for_next=False):\n",
" this_cell = \"\"\"$('div.cell.code_cell.rendered.selected')\"\"\"\n",
" next_cell = this_cell + '.next()'\n",
"\n",
" toggle_text = 'Toggle show/hide' # text shown on toggle link\n",
" target_cell = this_cell # target cell to control with toggle\n",
" js_hide_current = '' # bit of JS to permanently hide code in current cell (only when toggling next cell)\n",
"\n",
" if for_next:\n",
" target_cell = next_cell\n",
" toggle_text += ' next cell'\n",
" js_hide_current = this_cell + '.find(\"div.input\").hide();'\n",
"\n",
" js_f_name = 'code_toggle_{}'.format(str(random.randint(1,2**64)))\n",
" \n",
" html = \"\"\"\n",
" <script>\n",
" function {f_name}() {{\n",
" {cell_selector}.find('div.input').toggle();\n",
" }}\n",
"\n",
" {js_hide_current}\n",
" </script>\n",
"\n",
" <a href=\"javascript:{f_name}()\">{toggle_text}</a>\n",
" \"\"\".format(\n",
" f_name=js_f_name,\n",
" cell_selector=target_cell,\n",
" js_hide_current=js_hide_current, \n",
" toggle_text=toggle_text\n",
" )\n",
"\n",
" return HTML(html)"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def lin_inter(x,y):\n",
" # part of the homework\n",
" \n",
" return splines\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def langrage(x: np.ndarray, y: np.ndarray) -> (np.poly1d):\n",
" # part of the homework\n",
"\n",
" return polynomial"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"def plot_piecewise(x,y,degree):\n",
" k = degree\n",
" f = []\n",
" for i in range(0,len(x), k):\n",
" l_x = []\n",
" l_y = []\n",
" for j in range(i, min(i+k+1, len(x))):\n",
" l_x.append(x[j])\n",
" l_y.append(y[j])\n",
" \n",
" x_min = x[i]\n",
" x_max = x[min(i+k, len(x) - 1)]\n",
" x_vals = np.linspace(x_min, x_max, 100)\n",
" ip = langrage(l_x,l_y)(x_vals)\n",
" f += (langrage(l_x,l_y)(l_x).tolist())\n",
" plt.plot(x_vals, ip)\n",
" \n",
" plt.show()\n",
" hide_toggle()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"<h3>Hermite Interpolation</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Problem bei stückweiser Polynominterpolation:\n",
"\n",
"Die Funktion hat 'Knicke' zwischen zwei Polynomen"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"x = [0,0.3,0.7,1,1.4,1.8,2,2.2,2.7,3,3.4,3.5,4]\n",
"y = [0,0.5,-.8,0.9,-0.6,0.3,0.1,0,-0.2,0.75,-0.4,0.4,0]\n",
"plt.rcParams['figure.dpi'] = 200\n",
"i = np.interp(np.linspace(0,4,100), x,y)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"scrolled": false,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1200x800 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
" <script>\n",
" function code_toggle_4857888143181549003() {\n",
" $('div.cell.code_cell.rendered.selected').find('div.input').toggle();\n",
" }\n",
"\n",
" \n",
" </script>\n",
"\n",
" <a href=\"javascript:code_toggle_4857888143181549003()\">Toggle show/hide</a>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"plt.scatter(x,y,s = 10, color='black')\n",
"plt.show()\n",
"hide_toggle()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1200x800 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
" <script>\n",
" function code_toggle_6347792271310739777() {\n",
" $('div.cell.code_cell.rendered.selected').find('div.input').toggle();\n",
" }\n",
"\n",
" \n",
" </script>\n",
"\n",
" <a href=\"javascript:code_toggle_6347792271310739777()\">Toggle show/hide</a>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"for i in range(len(x) - 1):\n",
" x_vals = np.linspace(x[i], x[i+1], 100)\n",
" ip = np.interp(x_vals, [x[i], x[i+1]], [y[i], y[i+1]])\n",
" plt.plot(x_vals, ip)\n",
"plt.scatter(x,y,s = 10, color='black')\n",
"plt.show()\n",
"hide_toggle()"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1200x800 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
" <script>\n",
" function code_toggle_13125961785695534932() {\n",
" $('div.cell.code_cell.rendered.selected').find('div.input').toggle();\n",
" }\n",
"\n",
" \n",
" </script>\n",
"\n",
" <a href=\"javascript:code_toggle_13125961785695534932()\">Toggle show/hide</a>\n",
" "
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"for i in range(len(x) - 1):\n",
" x_vals = np.linspace(x[i], x[i+1], 100)\n",
" ip = np.interp(x_vals, [x[i], x[i+1]], [y[i], y[i+1]])\n",
" plt.plot(x_vals, ip)\n",
"plt.show()\n",
"hide_toggle()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"from IPython.display import Video"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"scrolled": false,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"text/html": [
"<video src=\"imgs/linear60.mp4\" controls >\n",
" Your browser does not support the <code>video</code> element.\n",
" </video>"
],
"text/plain": [
"<IPython.core.display.Video object>"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Video(\"imgs/linear60.mp4\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Ein Polynom vom Grad 1 genüg offensichtlich nicht, da wir keine weiteren Anforderung an dieses setzen können.\n",
"\n",
"Also brauchen wir ein Polynom höheren Grades.\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Problem ? "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Wir haben nur 2 Gleichungen:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"p_j(x_j) = y_j \\\\\n",
"p_j (x_{j+1}) = y_{j+1}\n",
"\\end{aligned}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Mit 2 Gleichungen können wir maximal ein Polynom von Grad 1 (eindeutig) bestimmen"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Also brauchen wir mehr Gleichungen!"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Erste Idee: nimm einfach mehr Punkte ."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"plt.scatter(x,y,s = 10, color='black')\n",
"plot_piecewise(x,y,2)\n",
"hide_toggle()\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"plt.scatter(x,y,s = 10, color='black')\n",
"plot_piecewise(x,y,3)\n",
"hide_toggle()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"plt.scatter(x,y,s = 10, color='black')\n",
"plot_piecewise(x,y,len(x))\n",
"hide_toggle()"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"text/html": [
"<video src=\"imgs/lagrange60.mp4\" controls >\n",
" Your browser does not support the <code>video</code> element.\n",
" </video>"
],
"text/plain": [
"<IPython.core.display.Video object>"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Video(\"imgs/lagrange60.mp4\")"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Dadurch werden unsere Intervalle größer, das Problem aber nicht gelöst."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Denn $n$ Punkte bestimmen ein Polynom vom Grad $n-1$ $\\textbf{eindeutig}$."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Also können wir immer noch keine weiteren Anforderungen treffen."
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Idee der Hermiten Interpolation:"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Die Funktion hat 'Knicke', da die Ableitung nicht stetig ist"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Also Iterpoliere neben den Funktionswerten auch noch die Ableitungen"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Dafür brauchen wir neben den Stützpunkten $\\vec{x}$ und den Funktionswerten $\\vec{y}$ auch noch die Ableitungen der Funktionswerte $\\vec{y} ^\\prime$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Bei der Interpolation von je 2 Datenpunkte und einer Ableitung kriegen wir dann zusätzlich die Gleichungen:\n",
"\n",
"$$p_j ^\\prime (x_j) = y_j ^\\prime \\\\\n",
"p_j ^\\prime (x_{j+1})= y_{j+1} ^\\prime $$\n",
"\n",
"Da die Ableitung linear ist, sind auch diese Gleichungen linear\n",
"\n",
"Insgesamt haben wir 4 Gleichungen, also bestimmen wir ein Polynom von Grad 3"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Sei $\\vec{x} = (1, 2)^T$, $\\vec{y} = (1, 2)^T$, $\\vec{y}^\\prime = (0, 1)^T$.\n",
"\n",
"Wir Interpolieren mit einem kubischen Polynom, also \n",
"\n",
"$$p(x) = a x^3 + b x^2 + c x + d$$ und\n",
"$$p ^\\prime (x) = 3a x^2 + 2b x + c $$\n",
"\n",
"\n",
"Wir haben die Gleichungen:\n",
"\n",
"$$p(x_0) = y_0 \\\\\n",
"p (x_{1}) = y_{1} \\\\ p ^\\prime (x_0) = y_0 ^\\prime \\\\\n",
"p ^\\prime (x_{1})= y_{1} ^\\prime $$\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Sei $\\vec{x} = (1, 2)^T$, $\\vec{y} = (1, 2)^T$, $\\vec{y}^\\prime = (0, 1)^T$.\n",
"\n",
"Wir Interpolieren mit einem kubischen Polynom, also \n",
"\n",
"$$p(x) = a x^3 + b x^2 + c x + d$$ und\n",
"$$p ^\\prime (x) = 3a x^2 + 2b x + c $$\n",
"\n",
"\n",
"Wir haben die Gleichungen:\n",
"\n",
"$$\\begin{aligned}\n",
"a x_0^3 + b x_0^2 + c x_0 + d = y_0 \\\\\n",
"a x_1^3 + b x_1^2 + c x_1 + d = y_{1} \\\\ \n",
"3a x_1^2 + 2b x_1 + c = y_j ^\\prime \\\\\n",
"3a x_1^2 + 2b x_1 + c= y_{1} ^\\prime \n",
" \\end{aligned}$$\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Sei $\\vec{x} = (1, 2)^T$, $\\vec{y} = (1, 2)^T$, $\\vec{y}^\\prime = (0, 1)^T$.\n",
"\n",
"Damit kriegen wir das LGS\n",
"\n",
"$$ \\left( \\begin{matrix}\n",
" x_0^3 & x_0^2 & x_0 & 1 \\\\ \n",
" x_1^3 & x_1^2 & x_1 & 1 \\\\ \n",
" 3x_0^2 & 2x_0 & 1 & 0 \\\\ \n",
" 3x_1^2 & 2x_1 & 1 & 0 \n",
" \\end{matrix} \\right) \n",
" \\left( \\begin{matrix} a \\\\ b \\\\ c \\\\d \\end{matrix} \\right) \n",
" = \n",
" \\left( \\begin{matrix} y_0 \\\\ y_1 \\\\ y_0 ^\\prime \\\\ y_1 ^\\prime \\end{matrix} \\right) \n",
"$$\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"Sei $\\vec{x} = (1, 2)^T$, $\\vec{y} = (1, 2)^T$, $\\vec{y}^\\prime = (0, 1)^T$.\n",
"\n",
"Mit Einsetzen:\n",
"\n",
"$$ \\left( \\begin{matrix}\n",
" 1 & 1 & 1 & 1 \\\\ \n",
" 8 & 4 & 2 & 1 \\\\ \n",
" 3 & 2 & 1 & 0 \\\\ \n",
" 12 & 4 & 1 & 0 \n",
" \\end{matrix} \\right) \n",
" \\left( \\begin{matrix} a \\\\ b \\\\ c \\\\d \\end{matrix} \\right) \n",
" = \n",
" \\left( \\begin{matrix} 1 \\\\ 2 \\\\ 0 \\\\ 1 \\end{matrix} \\right) \n",
"$$\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Lösen des Systems ergibt:\n",
"$$\\vec{c} = (4, -7, \\ 5,-1)^T$$\n",
"\n",
"Also ist unser Polynom\n",
"$$p(x) = 4x^3 + -7x^2 + 5x - 1$$"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"def hermite(x: np.ndarray, y: np.ndarray, yp: np.ndarray) -> list: \n",
" # part of the homework\n",
" return spline\n",
"\n",
"def plot_spline(points, interpolations):\n",
"\n",
" plt.scatter(points[0], points[1], color=\"black\")\n",
" # Plot piecewise interpolants\n",
" for i in range(len(points[0]) - 1):\n",
" # plot local interpolant\n",
" p = interpolations[i]\n",
" px = np.linspace(points[0][i], points[0][i + 1],100 // len(points[0]))\n",
" py = p(px)\n",
" plt.plot(px, py, '-')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [],
"source": [
"x_h = np.array([1,2])\n",
"y_h = np.array([1,2])\n",
"yp_h = np.array([0,1])\n",
"points = [x_h, y_h]\n",
"splines = hermite(x_h, y_h, yp_h)\n",
"plot_spline(points, splines)\n",
"plt.show()\n",
"hide_toggle()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [],
"source": [
"values = np.random.rand(3,6)*10\n",
"values[0] = np.arange(0,6)\n",
"values[1,1:3] = [1,2]\n",
"values[2,1:3] = [0,1]\n",
"points = [values[0], values[1]]\n",
"splines = hermite(values[0], values[1], values[2])\n",
"plot_spline(points, splines)\n",
"plt.show()\n",
"hide_toggle()"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Vorteil der Hermiten Interpolation:\n",
"\n",
" die Funktion ist stetig\n",
" \n",
" die einzelnen Polynome sind unabhängig voneinander\n",
" \n",
" \n",
"Nachteil:\n",
" \n",
" Wir müssen Ableitungswerte gegeben haben\n",
" Für viele Anwendung nicht möglich\n",
" können aber z.B alle Ableitungen auf Null setzen oder approximieren\n",
" "
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"<h3>Kubische Splines</h3>"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"weiterer Ansatz zum Lösen der 'Knicke' bei stückweiser Polynominterpolation"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Idee der Hermiten Interpolation:\n",
"\n",
"Die Funktion hat 'Knicke', da die Ableitung nicht stetig ist"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Stetigkeit können wir fordern durch:\n",
"$$\\lim_{x \\to x_0} f(x) = f(x_0)$$\n",
"\n",
"unsere kritischen Stellen $x_0$ sind die Stützpunkte der Polynome"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"wir betrachten \n",
"\n",
"$$\\lim_{x \\nearrow x_0} f(x) = \\lim_{x \\searrow x_0} f(x)$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"und damit bei uns\n",
"\n",
"$$\\ p_j^\\prime(x_{j+1}) = p_{j+1}^\\prime(x_{j+1})$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Wir brauchen keine Ableitungswerte mehr!"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Wir möchten wieder mit einem kubischen Polynom interpolieren"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Wir haben weiterhin unsere 2 Gleichungen:\n",
"$$\n",
"\\begin{aligned}\n",
"p_j(x_j) = y_j \\\\\n",
"p_j (x_{j+1}) = y_{j+1}\n",
"\\end{aligned}\n",
"$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Da wir noch 2 offene Freiheitsgräde haben, fügen wir die Gleichungen\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"p_j^\\prime(x_{j+1}) = p_{j+1}^\\prime(x_{j+1}) \\\\\n",
"p_j''(x_{j+1}) = p_{j+1}''(x_{j+1})\n",
"\\end{aligned}\n",
"$$\n",
"\n",
"hinzu"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"\n",
"Wichtig: Die Gleichungen sind nicht mehr unabhängig"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Da die Gleichung von einander abhängen, haben wir nun ein großes LGS für alle Polynome\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Unser Parametervektor ist $$\\vec{c} = (a_0, b_0, c_0, d_0, a_1 ,..., d_{n-1})^T$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Wir haben:\n",
"$$\n",
"p(x_j) = a_j x_j^3 + b_j x_j^2 + c_j x_j + d_j \\\\\n",
"p'(x_j) = 3a_j x_j^2 + 2b_j x_j + 1 \\\\\n",
"p''(x_j) = 6a_j x_j + 2b_j \\\\\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Wir formen die Gleichung \n",
"$$\n",
"p_j^{(n)}(x_{j+1}) = p_{j+1}^{(n)}(x_{j+1})$$ um zu\n",
"$$\n",
"p_j^{(n)}(x_{j+1}) - p_{j+1}^{(n)}(x_{j+1}) = 0$$"