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Created March 19, 2018 16:41
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bisezione.ipynb
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"### Metodo della bisezione\n",
"Il metodo pi\u00f9 immediato per approssimare $\\alpha$ \u00e8 il metodo di bisezione, che procede\n",
"suddividendo, ad ogni passo, l\u2019intervallo [a, b] a met\u00e0 e determinando in quale dei\n",
"due sottointervalli si trova la soluzione.\n",
"Si pone $a_0$ = a, $b_0$ = b. Per i = 0, 1, $\\dots$ si calcolano\n",
"\n",
"$$x_{i+1}=\\frac{a_i+b_i}{2} \\quad e \\quad f(x_{i+1});$$\n",
"$$se \\enspace f(a_i)f(x_{i+1}) < 0, \\enspace si \\enspace pone \\enspace a_{i+1}=a_i \\enspace e \\enspace b_{i+1}=x_{i+1};$$\n",
"$$se \\enspace f(a_i)f(x_{i+1}) > 0, \\enspace si \\enspace pone \\enspace a_{i+1}=x_{i+1} \\enspace e \\enspace b_{i+1}=b_i;$$\n",
"$$se \\enspace f(x_{i+1}) = 0, \\enspace \\alpha = x_{i+1}.$$\n",
"\n",
"Se la condizione $f(x_{i+1}) = 0$ non \u00e8 mai verificata, il procedimento definisce una successione di intervalli $[a_i, b_i]$ contenenti $\\alpha$, ciascuno di lunghezza met\u00e0 del precedente. \n",
"Quindi la successione dei $x_i$ converge ad $\\alpha$.\n",
"Il procedimento viene interrotto utilizzando un criterio di arresto: di solito si impone che\n",
"$$b_i\u2212a_i < \\epsilon,$$"
]
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"cell_type": "markdown",
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"source": [
"Esempio. Si traccia il grafico\n",
"della funzione $f(x) = x^3 \u2212 3x^2 + 1$ nell\u2019intervallo [0,1].\n",
"\n"
]
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"input": [
"%matplotlib inline\n",
"def f(x):\n",
" return x**3 - 3*x**2 + 1\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"x = np.linspace(0,1,100)\n",
"plt.plot(x,f(x))\n",
"\n",
"# plot marker for every 4th point\n",
"plt.samples = x[::5]\n",
"plt.grid()\n",
"# set the axis and legend\n",
"plt.axis([0,1,-1,1])\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
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"text": [
"<matplotlib.figure.Figure at 0x7fa2ed495a90>"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"Appare evidente che l\u2019equazione ha una sola soluzione reale $\\alpha$ $\\in$ (0, 1). Poich\u00e9 $f (0) > 0$ e $f (1) < 0$, si pu\u00f2 applicare il metodo di bisezione. Ponendo tol uguale a $10^{\u22123}$ si ottiene la successione"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"\n",
"def f(x):\n",
" return x**3 - 3*x**2 + 1\n",
"\n",
"n = 10\n",
"tol = 10**(-3)\n",
"\n",
"a = 0\n",
"b = 1\n",
"d = np.sign(f(a))\n",
"i = 0\n",
"ind = 1\n",
"lx = []\n",
"ly = []\n",
"size = [] # buble\n",
"while ind and i < n:\n",
" i = i + 1\n",
" x0 = (a+b)/2\n",
" f0 = f(x0)\n",
" if d*f0 > 0:\n",
" a = x0\n",
" else:\n",
" b = x0\n",
" ind = b-a > tol\n",
" lx.append(x0)\n",
" ly.append(f0)\n",
" size.append((n-i)*25) # buble\n",
" \n",
"print(\" {:4s} {:10s}{:10s}\".format(\"i\",\"xi\",\"f(xi)\"))\n",
"for i in range(n):\n",
" print(\"{:4d} {:10.5f} {:10.5f}\".format(i,lx[i],ly[i]))\n",
" \n",
"#plt.plot(lx,ly,'*')\n",
"#size = 50*np.random.randn(1000) \n",
"plt.scatter(lx, ly, s=size)\n",
"\n",
"plt.grid(True)\n",
"# set the axis and legend\n",
"plt.axis([0.48,0.76,-.32,.45])\n",
"#plt.axis([0,1,-1,1])\n",
"plt.title('Metodo della bisezione')\n",
"plt.xlabel('$x$')\n",
"plt.ylabel('$f(x)$')\n",
"#\n",
"x = np.linspace(0,1,100)\n",
"plt.plot(x,f(x))\n",
"plt.annotate(\"Root approximately at %.3f\" % x0,\n",
" fontsize=14, family=\"serif\",\n",
" xy=(x0, f0), xycoords='data',\n",
" xytext=(-150, +50), textcoords='offset points', \n",
" arrowprops=dict(arrowstyle=\"->\", connectionstyle=\"arc3, rad=-.5\"))\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" i xi f(xi) \n",
" 0 0.50000 0.37500\n",
" 1 0.75000 -0.26562\n",
" 2 0.62500 0.07227\n",
" 3 0.68750 -0.09302\n",
" 4 0.65625 -0.00937\n",
" 5 0.64062 0.03171\n",
" 6 0.64844 0.01124\n",
" 7 0.65234 0.00095\n",
" 8 0.65430 -0.00421\n",
" 9 0.65332 -0.00163\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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KlCnD0qVLWbRoEcOHD/f6sxg/fnyGq4Y2btzIiBEjsi1/xRVXULVqVd58800W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\ncPXV8Mwzzoi6wSCY+jS6AdNc76cB12Y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"text": [
"<matplotlib.figure.Figure at 0x7fa2d644e748>"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}
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