{ "cells": [ { "cell_type": "markdown", "id": "5b03aa44", "metadata": {}, "source": [ "# Cálculo de autovalores\n", "#### https://meet.noysi.com/metodosnumericos1" ] }, { "cell_type": "markdown", "id": "45aa23c7-93ab-4aa9-9d99-034f3b5b622d", "metadata": {}, "source": [ "## Teorema de Gersgorin" ] }, { "cell_type": "markdown", "id": "8b0f9d74-f584-45e7-bbdc-1caf53f0ff41", "metadata": {}, "source": [ "La siguientes funciones calculan los discos del Teorema de Gersgorin y los representan." ] }, { "cell_type": "code", "execution_count": 1, "id": "a502845e-5ac5-4221-9f93-3f24dc372fb7", "metadata": {}, "outputs": [], "source": [ "def Gershgorin(A):\n", " return zip(A.diagonal(),vector([sum([abs(k) for k in fila]) for fila in A])-vector(map(abs,A.diagonal())) )\n", "def discosG(A):\n", " B=matrix(CDF,A)\n", " cr=Gershgorin(B)\n", " discos= sum([ circle([c.real(),c.imag()],r,fill=true,alpha=0.2) for c,r in cr])\n", " return discos" ] }, { "cell_type": "code", "execution_count": 2, "id": "85ac3292", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n", "4 & -1 & 1 \\\\\n", "-1 & -3 & 1 \\\\\n", "1 & 2 & 5\n", "\\end{array}\\right) \\left[-3.426743094681910?, 3.757942566075653?, 5.668800528606257?\\right]$$" ], "text/plain": [ "[ 4 -1 1]\n", "[-1 -3 1]\n", "[ 1 2 5] [-3.426743094681910?, 3.757942566075653?, 5.668800528606257?]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = matrix([[4,-1,1],[-1,-3,1],[1,2,5]])\n", "show(A,A.eigenvalues())\n", "discosG(A)" ] }, { "cell_type": "code", "execution_count": null, "id": "f36b686f-e381-470e-bb94-d0554908757c", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "d712e005-e37e-4890-bf70-34fbe810b8f0", "metadata": {}, "source": [ "
\n", " Ejercicio 1. \n", "\n", "a) Aplicar el Teorema de Gersgorin para localizar los autovalores de la matriz \n", "$$A=\\left(\\begin{array}{rrr} 15.0 & -1.0 & 1.0 \\\\ 2.0 & -5.0 & 1.0 \\\\ 1.0 & 1.0 & -3.0 \\end{array}\\right). $$\n", "\n", "b) Aplicar el método de la potencia para aproximar el autovalor de módulo máximo. En cada paso, normaliza el vector. Detener el método cuando $\\|A v_k - \\lambda_k v_k\\|_2<10^{-2}$, donde $\\lambda_k$ es el autovalor aproximado obtenido y $v_k$ es el vector normalizado correspondiente a dicha iteración (que es una aproximación del autovalor). Aplicar el método con varios pasos y representar los valores obtenidos para $\\|A v_k - \\lambda_k v_k\\|_2<10^{-2}$. \n", " \n", "c) Aplicar el método de la potencia para aproximar el autovalor de módulo máximo, pero tomando como vector inicial uno de los autovectores correspondientes a un autovalor que no sea el de módulo máximo (calcúlalo con la función de Sage `eigenvectors_right`. Realizar $100$ iteraciones del método y representar el error residual $\\|A v_k - \\lambda_k v_k\\|_2$. \n", "\n", "d) Aplicar el método de la potencia inversa para aproximar el autovalor de módulo mínimo, con las mismas consideraciones que en el apartado b).\n", "\n", "e) Aplicar el método de la potencia inversa desplazada para encontrar el autovalor restante, con las mismas consideraciones que en el apartado b).\n", " \n", "
" ] }, { "cell_type": "code", "execution_count": 66, "id": "ca76b526", "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/latex": [ "$$\\newcommand{\\Bold}[1]{\\mathbf{#1}}\\left(\\begin{array}{rrr}\n", "15.0 & -1.0 & 1.0 \\\\\n", "2.0 & -5.0 & 1.0 \\\\\n", "1.0 & 1.0 & -3.0\n", "\\end{array}\\right) \\left[14.958148652677082, -2.639723010334766, -5.318425642342307\\right]$$" ], "text/plain": [ "[15.0 -1.0 1.0]\n", "[ 2.0 -5.0 1.0]\n", "[ 1.0 1.0 -3.0] [14.958148652677082, -2.639723010334766, -5.318425642342307]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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LHA6ZS6i/f/n9di+//DLuuecetLS0wGaz4bnnnsvreXv37kVfXx+OHDmyvBcmIjKBREIG8QGSjaLFNTZK29HZs/r02xUlsIvHJWCxSr+YFlIpabxUFGtP2uzz5RZULgS3W4LF06eXN51KJBLBDTfcgO985zuFOSAiIgs5eza3hCXlx26X90td073YijI2dXxcmtw7OorxauY0NCRzA61apfeRaKu8XLJ1ExOFK8s3NAADAzK/3datSyth79q1C7t27SrMgRARWcilS1IRqa8vvQmIV8rjkdHDJ0/KrBDFrFZq/qNSJ9l1u63XM1Yo4bCsxOH3l8bJU1kpgV2h+g9sNrk7GhiQ4FhLiUQCoVBo1kZEZDXqYgKKYv4pt/TS0CAzgQwOFvd1NQ8jIhEpvVVVaf1K5qQoMnw8kZAIvxS43RLUrXROu6v3mU7LGsRa9jQcOHAAfr//ytbe3q7dixER6WR0VPqhufTn8tntkrA5f15ioaK9rtYvEAhI75OV+8ZWIhSSk6eURgurWclCz0HX0CDZYS2HmT/yyCMIBoNXtot6T1hERFRgqZSUYLmYwMr5/VKSLealQvPAbnxc+qpoLkWREmwmU3qjhT0eKZum04Xbp9MpQWN/v7ynWnA6nfD5fLM2IiIrGRmR/jqrzaWqB5tNpom5cKFwgwYXo2lgp640wDLs/Kanpf5eStk6lccjqelClmMBafIdG9O+146IyIrSaQlCvF5rTrulh8pKWVFqZKQ4r6dpYBcIyH+mVHrHlmpiQk6iUpzwUf2FMT1d2P2Wl+cyofkIh8Po7e1Fb28vAKC/vx+9vb0YGBhY8HmcoJiIrOjyZbkxLsWEg5Z8PhlEkUho/1o2RdGu1byvT2arbmvT6hXMKx4Hjh2TAKdURxwFAtJ7ef31hR0NHIlIX+ftty8+oeahQ4dw5513zvn6Aw88gIMHDy76WqFQCH6/H8FgkGVZIjK9N96QfrDWVr2PxFqyWQnsuru1j4k0a4tUFMlIMVs3PzWbafV56xbidst7kEgUdnCN1yt3nWNjiwd2O3fuhIb3NkREphEKyWjYmhq9j8R67HbpA794EWhp0XZqM812HYtxNOy1KIo0plZUlPbcfhUVQDK5vBUjFuP1yt2RVoMoiIis5vJl+X3MhIw2amrkPS70jBBX0yywi0al3Oh0avUK5hWNSm9ZqZZgVTabBLlaLJRcVSXvMecPJiJanKJIto5BnXYqKmQqGVMHdopSGispLFU4LJkqBr0yR1KhR8YC2p9AHDxBRFYSDkuL0GLtK7QybrcE0Fp2AGkWdgWDHCp9LZOTnPRR5XRKVi2bLfy+XS7tTqC9e/eir68PR44cKfzOiYiKLBiU6gnbp7RVWSkBtJYrUWgS2CmKBC+lNuluPhIJOYGY7hZqn50WQ8CrqrQ/gYiIrGBigosJFIO6pKaW5VhNArtYTA6cgd1csZgEMXxvhBrYadFn53LJex2NFn7fRERWkclIMobZuuKw2Qo/h+tMmgR2yaT0N5XixLuLicel7MjeQ6GOCk6ltNm3ojBjR0S0EHWwIwO74nC5tF0dSZPwIpWSOwD22M0VjTKom08h14ydqbxcm5Q3B08QkVVEo5KQYTKmOFwuSThotQqFZoGdopT2HG3zURQJMjgadq5kUpv9ulzA1FThB2dw8AQRWYVa1eA1uzhcLsmQalVN0iywo7nSad4VzaesTJseO0CCaK16+IiIrGB6mgMniqmsTKqaWl2XNOuxo7nSadlYop7N4dAuJV1eLu85bzaIiOYXi3EKLj1odV3SbFQsPyRzpdPsPZyPwyEfcC3msnM4tAns2GNHRFagrv7Da3bxaZUEY2BXRAzs5qcGX1qs66qOjC10YMceOyKyglRKfv/yml1cZWXarJMOaBTYZbNswpxPOs33ZT7qKGEtMnYqlmKJiOZiYKcP0wV2HBE7v2xW2/XhzErNqmn53mgZNBIRmVU2y7lV9WC3a1OlAoC8YnRFUTC9hGmSp6ftiMVscDoZxcwUidgQj9sRjfJ9mSmRAOJxGyKRjCbz2UWjNoRCWYRCK3/fE4kEEjNGeqjnRSgUWvG+iYiKbXoaiEQcqKhQOPCxiKJRGxRFQSi0tKxDVVUVbItkzmyKsnieJBQKwe/3L+GlbwPgBjC1hOeUglUANgEY0/tADMYJ+bz0AtBi/HcbgDcBnNdg30REZlYF4N0ALgPQaKZ4mkcNgBiAV5b0rGAwCJ/Pt+Bj8srYVVVVIbiE6ft//Ws7PvnJh/DjHz+X93OW4k/+5E/w7LPParJvLfd//nwMe/YcwLe+9Xdwa7R2y2OPfRn79/8vU+07kQASCRv+9m/34Ec/+kHB9z80ZMNf/dU96O09tuJ9XZ2xGxkZwS233IK+vj60traueP/z6e7u1myQhpb71nr/Wu47FAqhvb0dFy9eXPSX6HLwfS/+/rX+mQLmfN+np4FbbvkcDh78v5rNsarVNTUSieB3fue38eKL/w9er7fg+we0O/bJSRv+/M8/ibfeWtrSSFVVVYs+Jq/AzmazLelEqKwEbDYHKisr837OUtjtds32reX+vV5Jn7rdbng8noLvHwBsNrvp9m23y+ZwaPW+y761+mUOyMmm1f4dDocp9631/rU+dgDw+XyavAbfd/32r9XPFDDn++5wyDXP46mEy1Xw3QPQ/prt9XpNF2/E44DdvrTYKl+atEs6HMDu3bu12DUA4KMf/ahm+9Zy/8WY5uTuu+823b7VZoD77vs9zfa/Z88farLvYti7d68p9631/rU+di3xfddv/1oy4/teVgbce+/vaLZeN6D9NVtLWh17Og18/OP3arLvvHrslurYMWBwEGhqKvSezW14OIzdu/8KTz31BCortcmqmVE4LH/edJM2we/Fi8DttwMNDYXf9+Dg4JXyTltbW+FfgHSh9hXn089C5sCf6fyyWeDwYfmzulrvo1macDiMnTvvwKFDhzXNCGphcBDYvBnYsKHw+9YkY+d2Q9Po36zc7gp88IMfgN3ORflmymRk6S8tgjp1CbdCr4Oorjzxvve9DwDgdDoL+wKkK6fTiccee4w/Vwvhz3R+drusqW3Ga3ZFRQU+/en/iQoTLsCuKNqtG69Jxu78eaC3F2hvL/SezS2ZBF5/XX6YGo2dMKXLl4G6Orl7KbR4XJqD3/Me6bUrNGYBiMjs3ngDGB5mla2YLl4EursBLcbcaZKxK3R2xCrKyiSo4yoIs2UycseohWRSPo+8SSciml9lJa9LxaSuzqXVdYmBXRHZ7UBVlXYL/5qVlinpeBzw+bhcDhHRtXi9XBWpmOJxwOUCNJrAQrvATl3YnWarrNRuGREz0+pmIJEAamq02TcRkRV4PKwmFVM8Lu1YWrVkaRLYVVTIhZqB3VzqPEFcu3Q2LTNqWvTWqYMnuru7C79zIqIi8nrl2hTXYuEfmiMel4TDIiuDLZsmgZ3LJbVjfkjmcrvlvWE5ViSTEtRp0WuQSMgNhhaB3d69e9HX16fpDPxERMVQXi5tQtGo3kdSGtJpYEmrtC6RZhMUV1czsJuP0ynl2L/4iy/jj//4D2dtP/vZT/U+vKJLJuU90WLG83BY+utMNr0R6WTfvn2w2WyztiYOEzSdl19+Gffccw9aWlpgs9nw3HPPzfq+oijYt28fWlpa4Ha7sXPnTpw4cUKfgzWQxkbjXrNff/11PPzww/jQhz6I7dtvxqFDv5z1/X37HsP27TfP2vbseUCno11YMilVTS0nUdCsAFZdDVy4oNXezctmk6k9FKUC9933P7Bz584r33NptZ6LgSUS8n5oUYqNRoHOThm0QpSPLVu24N/+7d+u/NtRjOViqKAikQhuuOEGfOITn8B999035/t//dd/jW984xs4ePAgNmzYgMcffxx33303Tp06ldc6nFZVXZ2rJhltWrhYLIYNGzZg9+7d+MIX/mLex+zYcRsee+yxK/8uN+gozulpyY6aMrDzeCSIURTt6shmVVUF2GxplJd7UF1d2p396bS8H1rs12bTbuBET08Penp6kOFIGEspKytjls7kdu3ahV27ds37PUVR8K1vfQuPPvoofu/3ZAnDZ555BqtWrcJPfvITfOYznynmoRqKWt2YnpabbSO5/fbbcfvtty/4mIqKCtTX1xfpiJYvFtM+4aDZrr1eifoTCa1ewby8XsBmi+HFF3+JBx/8DL70pS/h+eefQzpdmkOStCrDVlZq18fAHjtreuedd9DS0oLOzk7cf//9OHfunN6HRAXU39+P0dFRfOADH7jyNafTiTvuuAOvvPKKjkemP7sdaGkBIhG9j2R5XnvtKO666y787u/+Lh5//CuYnJzU+5Dm0DrhoNIsY+d250bZlGCFcUF2O/CRj9wGl2sL2tsrcO7cWfzsZz/D+Pg4/vRPP6334RWNOnBCi8/H9DSwaRPnVKT83XrrrXj22WexYcMGjI2N4fHHH8dtt92GEydOoM5oKQxaltHRUQDAqlWrZn191apVuMDeIdTWyu9kI5ZjF3LbbbfjrrvuQlNTM4aHh/HUU0/hwQcfxI9+9CNDLTcWDEqyQes1eTUL7BwO+ZAMDJhvYeHlevrpp/G97313wcc8++z/QVdXFz7xiY/g2DEJgDs6OuDxePHtb/8tPvax+0umzyORkKCu0HP5xOMS0F31u5toQTPLd9u2bcOOHTuwdu1aPPPMM/jc5z6n45FRodmu6g9SFGXO10pRTQ3Q0ABMTprr9+fMDOy6devQ1bUZH/7wh/GrX/3qynreRhAOA+vXaz9hvqa7r68Hzp0rnT67j33so/jgBz+w4GOam1sASDm2rg4YG5PgZt26dQCAS5dGSyawi0aBjg65CSikQEB+OZXKDQVpw+v1Ytu2bXjnnXf0PhQqELV/cnR0FM3NzVe+funSpTlZvFJktwNtbcDIiMy1ataBZ/X1DWhqasbAwIDeh3JFOCzX/YYG7V9L08DO75dBFLGYdktnGEl1dc2SBkM0NACjo1J3V8sA1SUSjagTNBe6By6TkTJCW5u2NxMcPGF9iUQCb7/9Nt7znvfofShUIJ2dnWhqasIvfvEL3HjjjQCAZDKJw4cP42tf+5rOR2cMDQ0ykCIUMu/NcSAQwNjYmKEGUwQCMmiiGNNvaRrYeb1y4Z6aKo3ALl9vvvkmjh8/jptu2o5UqgaHDg3i+ef/N2688WbU1RUhnDeAWEwylYX+kE9NSQtAvufzV7/6Vbz44ovo7e1FRUUFAoFAXs/bu3cv9u7di1AoBL+WM01S0Xz+85/HPffcg46ODly6dAmPP/44QqEQHnjAmPNh0fzC4TDOnDlz5d/9/f3o7e1FbW0tOjo68PDDD+OJJ57A+vXrsX79ejzxxBPweDz4gz/4Ax2P2jicTqmkHD8u128jVNui0SguXrx45d9DQ8M4deoU/H4ffD4/vvvdp/G+970f9fX1GB4eRk9PD6qrq3HnnXfqeNQ58bhUplpaivN6mgZ2NhvQ1CRpXcqpqCjHL37xEr73ve8ikfDB778d733v+7B792/rfWhFE4vJhJiFXHEinZb9dnXl3/ibTCbx+7//+9ixYwd+8IMfFO5gyHQGBwfx8Y9/HBMTE2hoaMC73vUu/PrXv8bq1av1PjRagqNHj866oKv9kQ888AAOHjyIL3zhC4jFYvjsZz+Lqakp3HrrrXjppZdKpgUmH21t0h8fCBhjre2+vj48+GBuKppvfvMbAIAPf/jD+Mu/fARnzpzBCy+8iHB4GvX19di+fTsOHDgArxbLDi3DxASwenXxppGxKYqiaPkCgQDwX/8lWRQDDU4xjGwW6OuTZtVi1N6NYnRUArBCtrWMjUnp4JZblt6cevDgQTz88MN5Z+xUasYuGAzCp+WMk0RERXTuHNDbC7S3m7fXzggiEemv27GjeEGy5j8un08moJ2e1vqVzMluB1pb5e+lsn5sIiGZukLeIKdSsnV2ajviKJFIIBQKzdqIiKymtVUyTAacDs5ULl+W0nYxM5+aB3Zq4BIOa/1K5lVdLWXJyUkZQWx1oZB8yAs5zcnYmPQvaD2w7cCBA/D7/Ve29vZ2bV+QiEgHTidw3XXS3lIqSYdCCwSkj7zY3RxFSbA2NspACrPOaK01m00ieq9Xgh4ry2Sk/NzQULim3EBABmJs2CA3EvMt5n71dvTo0WW91iOPPIJgMHhlm9nQS0RkJa2tUoodG9P7SMwnlZLr+YYN2iybuRCNp8kTVVWSSRkYkOCF5vJ4JLg7eVIyWVbtRwyH5fNQqGH06bScPL/1W7mpU/7sz/4M999//4LPW7NmzbJez+l0wlnIER9ERAZlt0tgMjUlmxEGUpjF2Jhc09vaiv/aRQnsAIn8BwbkQqz1rMtm1dgo2aeREQmEjTDMvNCiUflFUajPwOionDgdHbmv1dfXG2r+IiIis6qqkt/Zr7+eWwOeFqZO8bZ+feEn4M9H0ca61NbKNjVVrFc0H7tdAhSfTxourSYalWxkbW1h9jc+Lv0LGzYs/+QZGBhAb28vBgYGkMlk0Nvbi97eXoQXaQrt6elBV1cXuru7l/fCREQm0dYmfWIjI9JOQ9cWjUrb2caNci3Xg+bTncw0MAAcPSrBixWzUYUSCMgUKGVlxa/Na0kd4LBhw8r3FQrJCXTzzTJX4nLt2bMHzzzzzJyv//KXv8TOnTvzOA5Od0JE1hePA2+8AVy6JBU4XsPnSqUk+N24Edi8Wb/3qKiBXSwGvPKKjPxkrX5ho6PAqVMS8btceh/NyiUSMuXNtm0r76+LxyVbd/31MmpLTwzsiKhUBIOSnEkmpXWIcrJZYHBQElc33KBvy1lRpx10u2WesVAot1YozW/VKvmABALWGGoeCMhI2JWuvpVMSuZv7VpgmeMfiIhoGfx+YOtWSc4scS53S1MUYHhYrnGbN+s/jqDo80lz0sP82GwyzLytTd4rMwd38bh80FtaVpaaTqXk5OnsBDZt4mzoRETFtmqVVF5iMQZ3QC6oq66W98Xj0fuIdAjsnE65MEejbMJcTFmZvFdtbTKYwqzBXSAgfXArqVQmk8DQkGTptmwByssLdXTLw8ETRFSq2tsZ3AG5oM7nk/LrSitShVLUHjtVKgX85jfSc8U6/eLSaaC/X+r31dXm6rmLROTnvW2bjGBdjnhcyq+dnRLUGWm4PXvsiKhUDQwAx4/LjXaxFrg3ikxGBkpUV0tQV6i5WQtBl2JWebk0vSeTctGnhamZu9WrpXnVLOvuKor0UzY3Lz+om56WgRLr10tvh5GCOiKiUtbRIZPDA5K5KpXeebWC1NAA3HijsYI6QKfADpA6fVMTlyrJlxrcbdwowbAZ1pUNhSSgW+50JBMTkvHbts0Y5VciIpqttRXYvl3KkYODUmGyskhEZq1Yswa46Sb95qpbiG6BncMh85m5XJKFosXZbJL92rxZMldjY8Y9iZJJKaGuXr300nE6Lb8gHA45cdau5UAJIiKjqq2V4K6tTTJZi8zvbkqKIsmGYBDo6pLptozaFqXr5bKmBli3Tt4oowYoRlRbKx+spib5oBmtNKsoklFsapJU9VIEg5LSb2qSXxTNzdoc40px8AQRUY7XK2XZri4J7Ky0SkU8Lv2E5eWSbFjJakfFoMvgiZnSaeC113JrflL+MhmZBfzCBfng1dXpP38OIMGZ3S49cfkO/U6n5TPgckmwv3q1Mf4vi+HgCSKi2cbHgdOnpapUV7f8Hmu9KYrMSKFWn9avlwDW6HS/dJaVSfQbCEhAYJThwmbgcEhGq6oKuHhRTqKyMmnk1OtuQi3Bbt6cX1CXyciJk0jI/2XDBq5KQkRkZupk9OfOyYwOgQBQX2/c0uV8gkE57upqSVI0N5unJUj3jJ3q7FngzTdlElszZGqMJpuV8ufQkPzpcklTZzE/iIqSWw92/fqFXzubBaampBG1vl5GSTc1GTu9PR9m7IiIrm1qSqpKg4Pye7+hwdizG4TDkmyoqpIBi62tsmqWmRgmhFq9WqLjgQEpyZolMjYKu10CpOpq+VAODUmZtrxcPqDFOJEmJyWY7Oi49s8vmZQTPZGQzNymTXInZLYRrz09Pejp6UHGKk0kREQaqKmR61Jbm2TvRkclwKuuNk6JNpORWRymp6XStGmTXMeMcnxLZZiMHSCrUbz2mgR4LS16H425pVISQI2NyfuZTsuH1OPRJmhW1//dvHnunD7ZrGTm1N67+nqZubyhQVYi0cv58+fxla98Bf/xH/+B0dFRtLS04I/+6I/w6KOPoiLPSJgZOyKi/KiVpZERGSQXich1yefT5+Y+FpPrUjIp1632dpmKraqq+MdSSIbJ2AESdGzdChw9KlmnUpvJupDKy2VVj4YGCbouX5YRtOPj8n23W97vQpS9YzHpq9u4MRfUpdOS0laHvXu9Um5taZE7OCNkZE+ePIlsNounn34a69atw1tvvYVPf/rTiEQi+PrXv6734RERWYp6Y6+234yPS5l2YkKSEW63BHpalT6zWUkgTU/nXq+hQbKJ9fXGLhEvhaEydqrhYcnc+XzmTYUaUSolH2g10FPX67XZ5AOtbg6HfC0fyaSUfFtb5QRJJOTkKSvLTU5cWysBn57ZuXw9+eSTeOqpp3Du3Lm8Hs+MHRHR8qll0GBQyrSBgCQKALkeuVyylZUtrQc7nZZrXjwuWyolgaXHI9cqtXXJ683/emcWhsrYqVpaJOh46y3JPJkhIDCD8nIJsmprJeUcicgHPhqVEysWk22+OQXVD/7M24BMRtLqzc1yovh8su/KSjlZqqrMNxAmGAyitrb2mt9PJBJIJBJX/h0KhYpxWEREluRwSBWnpkZ67SMRqfREo9JOpI5OTadnL1l2dTB2dYrK4cgFho2NMkrX45HrkplG5y6HYS+7nZ3yAz57VgI9szXXG53DIYHYzCRTMilbOj17y2ZzJ43NJnc9druk0bduBW6+2TwZuYWcPXsW3/72t/E3f/M313zMgQMHsH///iIeFRFRabDZJDEws1KXTkvCIZWavWUyuWuTel0qK5NgrrxcNjWwM0LrTzEZshSrSqUka9ffz+DOSBRFRt3W1clM40Yrl+/bt2/R4OvIkSPYvn37lX8PDw/jjjvuwB133IHvf//713zefBm79vZ2lmKJiMgQDB3YAZJBOn5cGixbW81X2rMaNairrZWgzoijhyYmJjAxMbHgY9asWQPXf+fjh4eHceedd+LWW2/FwYMHYV/C7R177IiIyEgMHyZVVEi5D5Dgjpk7/WSzMrClpga44QZjBnUAUF9fj/r6+rweOzQ0hDvvvBM333wzfvjDHy4pqCMiIjIawwd2gPRubdsmdfL+fmnWt8qwZLPIZCSoq683dlC3FMPDw9i5cyc6Ojrw9a9/HePqXDAAmpqadDwyIiKi5TFFYAfkMnc2mwR3dXXmWIzXCpJJmVCyqQm4/nrj9dQt10svvYQzZ87gzJkzaGtrm/W9xToUuPIEEREZkeF77K6WyQBnzgCnTsnQZS4Yr61IROa8W7NGVpWw+jDxpWKPHRERGYnpGoocDmDDBuCmmyTIGxmZO38NFcbUlMwf1NUlpXAGdURERMZmusAOkHJsWxuwfbv0eg0Ozj+pLi2PosgM4JkMcOONEkhzNDIREZHxmTKwU9XVyeS4LS0yBYe6LiktXyIBXLwofXQ33ywrVFhtuZVC6OnpQVdXF7q7u/U+FCIioitM12M3n2RSBlScOSPZpsbGpa0pR/K+TU7KDN+rVwPr13NwSj7YY0dEREZiiQJbRQWwcaNk8E6fltJsXZ11Rm9qLZEAxsZkeTE1A8rp3IiIiMzHEoGdqr5eghM1ezc9zezdQmZm6To7gXXrGAwTERGZmaUCO2B29u7UKcneVVXJtCjsFcuZnpagzu9nlo6IiMgqLBfYqdTs3cgIcPYsMDAgQYzfX9oBXjQKTEzIHIBdXUBHh/ydloYTFBMRkRFZYvDEYuJxydz190umqhT77+JxCejKy2Wk6+rVEvjSynDwBBERGYllM3YzuVzSP9bcLFN5XLggZUifTzYrlyDDYZlk2OGQ7NyaNVytg4iIyKpKIrBTeb3Apk3STzYyIlm8wUHA6ZRgp6JC7yMsjHQaCAYlqPN6JZhrbZVMZSmXoYmIiKyupAI7lZqpW7MGGB+XLN7EBJDNSg+e12vOLF4sJsuAZbNAdbVkKRsbS6/sTEREVKpKMrBTOZ2yNFlLiwREw8OylNbQkGS2KitlM+pyWtksEIlIZi6VAtxu+b+0tsrgEaMetxVw8AQRERlRSQyeWIpYTMqYly/LpL3T0zLfm9stQZ7TqW85M5GQY1SXT/N4gIYGCeSqqyXbyHJr/nbv3o3e3l5cunQJNTU1uOuuu/C1r30NLS0teT2fgyeIiMhIGNgtIJWSIC8QkExeOCyBVTYro0vdbhmYoVWwl0jIaNZ4XI5FUaQP0O0GVq2Snjm/X46Blueb3/wmduzYgebmZgwNDeHzn/88AOCVV17J6/kM7IiIyEgY2OUpm5VMWSQic8EFg1K+jcclAFPfRZtNSqAzN7s9F/jZbPJYdUunZ2/ZbO411eDR75fBHR6PbF4vV9PQyj/90z/h3nvvRSKRQHl5+aKPZ2BHRERGwi6sPNntElB5vbmvqcFeNAokk5JVSyTk37GY/D2ZzAVxM9lssjkcEqy53bkMYEVFLqjzeNgrVyyTk5P48Y9/jNtuu+2aQV0ikUAikbjy71AoVKzDIyIiWhRDhhWYL9ibKZvNZeHUwE5RckGdmt1j9k1fX/ziF/Gd73wH0WgU73rXu/DCCy9c87EHDhzA/v37i3h0RERE+WMplixn3759iwZfR44cwfbt2wEAExMTmJycxIULF7B//374/X688MILsM3TODlfxq69vZ2lWCIiMgQGdmQ5ExMTmJiYWPAxa9asgWueUSeDg4Nob2/HK6+8gh07diz6WuyxIyIiI2Epliynvr4e9fX1y3quep8zMyu3kKqqKgSDQVRVVS3r9YiIiAqJGTsqWa+++ipeffVVvPvd70ZNTQ3OnTuHL3/5yxgZGcGJEyfgdDr1PkQiIqIlMeHCWUSF4Xa78Y//+I94//vfj40bN+KTn/wktm7disOHDzOoIyIiU2LGjoiIiMgimLEjIiIisggGdkREREQWwcCOiIiIyCIY2BERERFZBAM7IiIiIotgYEdERERkEQzsiIiIiCyCgR0RERGRRTCwIyIiIrIIBnZEREREFsHAjoiIiMgi/j/P5/GeERY51QAAAABJRU5ErkJggg==\n", "text/plain": [ "Graphics object consisting of 3 graphics primitives" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = matrix(CDF,[[15,-1,1],[2,-5,1],[1,1,-3]])\n", "show(A,A.eigenvalues())\n", "discosG(A)" ] }, { "cell_type": "code", "execution_count": 67, "id": "ec27e24b", "metadata": {}, "outputs": [], "source": [ "x0 = vector(CDF,[1,1,1])" ] }, { "cell_type": "code", "execution_count": 68, "id": "939b8e9c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((0.9890707100936804, -0.1318760946791574, -0.0659380473395787),\n", " 4.0,\n", " 11.452168961076477)" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x1 = A*x0\n", "l1 = x0.conjugate()*x1/(x0.conjugate()*x0)\n", "x1 = x1.normalized(2)\n", "x1, l1, (A*x1 - l1*x1).norm(2)" ] }, { "cell_type": "code", "execution_count": 69, "id": "2667f08a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((0.9830454953247029, 0.16964059432594433, 0.06959614126192587),\n", " 14.330434782608696,\n", " 1.3641109299063303)" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x2 = A*x1\n", "l2 = x1.conjugate()*x2/(x1.conjugate()*x1)\n", "x2 = x2.normalized(2)\n", "x2,l2, (A*x2 - l2*x2).norm(2)" ] }, { "cell_type": "code", "execution_count": 70, "id": "29a1b1bc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((0.9946788632828879, 0.08064963756347739, 0.06410612216584102),\n", " 14.664465593249199,\n", " 0.5678578314868246)" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x3 = A*x2\n", "l3 = x2.conjugate()*x3/(x2.conjugate()*x2)\n", "x3 = x3.normalized(2)\n", "x3,l3, (A*x3 - l3*x3).norm(2)" ] }, { "cell_type": "code", "execution_count": 77, "id": "80bc71ba", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(0.9890707100936804, -0.1318760946791574, -0.0659380473395787) 4.0 11.452168961076477\n", "(0.9830454953247029, 0.16964059432594433, 0.06959614126192587) 14.330434782608696 1.3641109299063303\n", "(0.9946788632828879, 0.08064963756347739, 0.06410612216584102) 14.664465593249199 0.5678578314868246\n", "(0.9922068082187079, 0.10986277687783112, 0.05878622271533068) 15.014030781336196 0.17404654734651825\n", "(0.9930530870692504, 0.10002059746958654, 0.06197940257907104) 14.934978256815933 0.06310418755874324\n", "(0.9927875014133826, 0.10343539489209777, 0.06061432273719322) 14.965593438416407 0.02206998184004376\n", "(0.9928793316010879, 0.10223756720332493, 0.06114010739050299) 14.955471635604079 0.007860072960139172\n", "(0.9928475990990809, 0.10266074715370238, 0.06094600854062709) 14.959084264861387 0.002787939112468266\n", "(0.9928587778578063, 0.10251078342012272, 0.06101628072322896) 14.957816131037632 0.000991264786188215\n", "(0.9928548289024103, 0.10256401805296372, 0.06099107251063016) 14.958266512849507 0.00035230293174870887\n" ] } ], "source": [ "x0 = vector(CDF,[1,1,1])\n", "# err = []\n", "for _ in range(10):\n", " x1 = A*x0\n", " l1 = x0.conjugate()*x1/(x0.conjugate()*x0)\n", " x1 = x1/x1.norm(2) # x1.normalized(2)\n", " x0 = x1\n", " print(x1, l1, (A*x1 - l1*x1).norm(2))\n", " # err.append((A*x1 - l1*x1).norm(2))" ] }, { "cell_type": "code", "execution_count": 81, "id": "3a033e0c", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 1 graphics primitive" ] }, "execution_count": 81, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list_plot(err,plotjoined=true)" ] }, { "cell_type": "code", "execution_count": 72, "id": "7a4c9a57", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[(14.958148652677082,\n", " [(0.9928558625160511, 0.10255006462425884, 0.0609977090804967)],\n", " 1),\n", " (-2.639723010334766,\n", " [(-0.03190857594998693, 0.36686740517079436, 0.9297258465827934)],\n", " 1),\n", " (-5.318425642342307,\n", " [(0.06518858130176128, 0.9057410148550928, -0.41878832705452773)],\n", " 1)]" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.eigenvectors_right()" ] }, { "cell_type": "code", "execution_count": 90, "id": "c837c556", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((-0.992855862516051, -0.10255006462425885, -0.06099770908049669),\n", " 14.958148652677076)" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x0 = vector(CDF,(-0.03190857594998693, 0.36686740517079436, 0.9297258465827934)) \\\n", " + 0.01*vector(CDF,(0.06518858130176128, 0.9057410148550928, -0.41878832705452773)) \n", "err = []\n", "aut = []\n", "for _ in range(100):\n", " x1 = A*x0\n", " l1 = x0.conjugate()*x1/(x0.conjugate()*x0)\n", " aut.append(l1)\n", " x1 = x1/x1.norm(2) # x1.normalized(2)\n", " x0 = x1\n", " err.append((A*x1 - l1*x1).norm(2))\n", "x1, l1" ] }, { "cell_type": "code", "execution_count": 91, "id": "db1a1ec9", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "Graphics object consisting of 2 graphics primitives" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "list_plot(err,plotjoined=true) + list_plot(aut,plotjoined=true,color='red')" ] }, { "cell_type": "code", "execution_count": null, "id": "84626a42", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "c34612fc", "metadata": {}, "source": [ "
\n", " Ejercicio 2. \n", "\n", "a) Utilizar el método de la potencia (desplazando los autovalores si es necesario) para calcular el radio espectral de la matriz\n", "$$M=\\left(\\begin{array}{rrr} 2.0 & -2.0 & 1.0 \\\\ 3.0 & 2.0 & 1.0 \\\\ 1.0 & 1.0 & -1.0 \\end{array}\\right).$$\n", "Dibuja en cada paso del método el módulo del error residual $\\|A v_k - \\lambda_k v_k\\|$ obtenido. Detener el método cuando $\\|A v_k - \\lambda v_k\\|_2<10^{-2}$.\n", " \n", "b) Calcula el resto de los autovalores.\n", " \n", "
" ] }, { "cell_type": "code", "execution_count": null, "id": "b01a43cb", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "4c444e21", "metadata": {}, "source": [ "
\n", " Ejercicio 3. \n", " \n", "a) Aplicar 10 pasos del método QR para aproximar los autovalores de la matriz \n", "$$\\left(\\begin{array}{rrr} 15.0 & -1.0 & 1.0 \\\\ 2.0 & -5.0 & 1.0 \\\\ 1.0 & 1.0 & -3.0 \\end{array}\\right). $$\n", "La factorización QR de cada paso, calcularla usando el método `QR` de Sage.\n", "\n", "b) Obtener una factorización QR de la matriz anterior, utilizando reflexiones de Householder. \n", " \n", "
" ] }, { "cell_type": "code", "execution_count": null, "id": "8a8d48d9", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "fb7ddc10", "metadata": {}, "source": [ "
\n", " Ejercicio 4. \n", " \n", "Encontrar una matriz tal que uno de los discos de Gersgorin no contenga ningún autovalor.\n", " \n", "
" ] }, { "cell_type": "code", "execution_count": null, "id": "76231cf2", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "SageMath 9.5", "language": "sage", "name": "sagemath" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.2" } }, "nbformat": 4, "nbformat_minor": 5 }