{ "cells": [ { "cell_type": "markdown", "id": "48dcfcc3", "metadata": {}, "source": [ "# Aitken's delta squared convergence acceleration\n", "What happens if you apply is to non-converging sums?\n", "I'm calling them \"ramanujan\" to honour the great mathematician Srinivasa Ramanujan.\n" ] }, { "cell_type": "code", "execution_count": 2, "id": "f8c15c06", "metadata": {}, "outputs": [], "source": [ "\n", "import itertools\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "from numpy import exp\n", "\n", "plt.rc('font', family='serif')\n", "\n", "def aitken(seq):\n", " \"\"\" \n", " apply Aitken's method to sequence seq with terms {s_i}\n", " s_i' = s_i - (s_i+1 - s_i)^2/(s_i+2 - 2 s_i+1 + s_i)\n", " \"\"\"\n", " s_i = next(seq) \n", " s_ip1 = next(seq) \n", " s_ip2 = next(seq) \n", " while True:\n", " yield s_i - (s_ip1 - s_i)**2/(s_ip2 - 2*s_ip1 + s_i)\n", " s_i, s_ip1, s_ip2 = s_ip1, s_ip2, next(seq)\n", "\n", "# 1-1+1-1...\n", "def ramanujan_A():\n", " sN = 0 \n", " for i in itertools.cycle([1,-1]):\n", " sN += i\n", " yield sN\n", "\n", "# 1-2+3-4+5-... \n", "def ramanujan_B():\n", " sN = 0\n", " j = 1\n", " for i in itertools.cycle([1,-1]):\n", " sN += i*j\n", " j += 1\n", " yield sN\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "0421b642", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Ramanujan summation\n", "sum of 1-1+1-1...\n", "last three values of Aitken accelerated sum: [0.5, 0.5, 0.5]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "sum of 1-2+3-4+5-... \n", "last three values of Aitken accelerated sum: [0.2512562814070378, 0.24875621890546995, 0.2512315270935943]\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", " \n", "if __name__=='__main__':\n", "\n", " N = 100\n", "\n", "\n", "\n", " \n", " print('Ramanujan summation')\n", " labs = [\"1-1+1-1...\",\"1-2+3-4+5-... \"]\n", " for ser, lab in zip([ramanujan_A, ramanujan_B], labs):\n", " res_orig = list(itertools.islice(ser(),N))\n", " res_ait = list(itertools.islice(aitken(ser()),N))\n", " \n", " x = range(N)\n", " plt.plot(x,res_orig,'ro-',label=ser.__name__)\n", " plt.plot(x,res_ait,'go-',label='Aitken accel.')\n", "\n", " print('sum of ',lab)\n", " print('last three values of Aitken accelerated sum:',res_ait[-3:])\n", " \n", " plt.legend()\n", "\n", " \n", " plt.xlabel('N')\n", " plt.xlim(-1,N)\n", " plt.show()\n" ] }, { "cell_type": "markdown", "id": "eced91ea", "metadata": {}, "source": [ "Using Aitken acceleration we found (approximately) \n", "$$\n", "A = 1-1+1-1+1- ... \\frac{1}{2}\\\\\n", "B = 1-2+3-4+5-... = \\frac{1}{4}\n", "$$\n", "Mark\n", "$$\n", "C=1+2+3+4+... \n", "$$\n", "and compute $B-C$ term by term:\n", "$$\n", "B-C = (1-1) + (-2-2) + (3-3) + (-4-4) + (5-5) + (-6-6) + ... \\\\\n", "= -4 -8 - 12 - ...\n", "= -4 (1+2+3+...) \n", "$$\n", "so \n", "$$\n", "B-C = -4C \\Leftrightarrow C = -B/3\\ .\n", "$$\n", "Since we found using Aitken acceleration that $B=1/4$, we get a strange result\n", "$$\n", "C = 1+2+3+4+5+... = -\\frac{1}{12} \\ .\n", "$$\n", "As a series this result does't make sense, but consider this: \n", "The Riemann zeta function at $-1$ has a mathematically well-defined value \n", "$$\n", "\\zeta(-1) = -\\frac{1}{12}\\ ,\n", "$$\n", "and since the series representation of Riemann zeta function is \n", "$$\n", "\\zeta(s) = \\sum_{n=1}^\\infty \\frac{1}{n^s}\\ ,\n", "$$\n", "so the *non-converging* series representation of $\\zeta(-1)$ is just \n", "$$\n", "\\zeta(-1) = 1+2+3+4+5 +... \\ . \n", "$$ \n" ] } ], "metadata": { "kernelspec": { "display_name": "python_env", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.15" } }, "nbformat": 4, "nbformat_minor": 5 }