cds-numerical-methods/Week 1/04 Runges Phenomenom.ipynb

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    "# CDS: Numerical Methods Assignments\n",
    "\n",
    "- See lecture notes and documentation on Brightspace for Python and Jupyter basics. If you are stuck, try to google or get in touch via Discord.\n",
    "\n",
    "- Solutions must be submitted via the Jupyter Hub.\n",
    "\n",
    "- Make sure you fill in any place that says `YOUR CODE HERE` or \"YOUR ANSWER HERE\".\n",
    "\n",
    "## Submission\n",
    "\n",
    "1. Name all team members in the the cell below\n",
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    "3. **restart the kernel** (in the menubar, select Kernel$\\rightarrow$Restart)\n",
    "4. **run all cells** (in the menubar, select Cell$\\rightarrow$Run All)\n",
    "5. Check all outputs (Out[\\*]) for errors and **resolve them if necessary**\n",
    "6. submit your solutions  **in time (before the deadline)**"
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    "## Runge's Phenomenom\n",
    "\n",
    "Use your own Lagrange interpolation routine to interpolate the function \n",
    "\n",
    "$$f(x) = \\frac{1}{1+25x^2}$$ \n",
    "\n",
    "between $x=-1$ and $x=+1$, using the $x_k$ below. Plot the results and briefly discuss their differences."
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    "# Import packages here ...\n",
    "\n",
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
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    "# Paste your Lagrange interpolation routine here ...\n",
    "\n",
    "# YOUR CODE HERE\n",
    "raise NotImplementedError()"
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   "source": [
    "### Task 1\n",
    "\n",
    "Use equidistant $x_k = \\frac{2k}{n} - 1$ with $k \\in \\{0, 1, \\dots, n  \\}$."
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    "### Task 2\n",
    "\n",
    "Use Chebychev nodes $x_k = \\operatorname{cos}\\left(\\frac{2k-1}{2n}\\pi \\right)$ with $k \\in \\{1, \\dots, n  \\}$."
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    "### Task 3\n",
    "\n",
    "Use $n$ randomly chosen points $x_k$."
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