{
"cells": [
{
"cell_type": "markdown",
"id": "22bbea85-88de-44d1-816b-a6556820a3e9",
"metadata": {},
"source": [
"# 2025-09-15 Stability\n",
"\n",
"* Forward and backward stability\n",
"\n",
"* Beyon IEEE double precision\n",
"\n",
"See [FNC](https://tobydriscoll.net/fnc-julia/intro/stability.html#backward-error)"
]
},
{
"cell_type": "markdown",
"id": "d7308ac2-799e-4826-afab-6cf8805dc6af",
"metadata": {},
"source": [
"## Wilkinson's polynomial\n",
"\n",
"$$ w \\left( x \\right) = \\prod_{k = 1}^{20} \\left( x - k \\right) = \\left( x - 1 \\right) \\left( x - 2 \\right) \\cdots \\left( x - 20 \\right) = \\sum_{k = 0}^{20} b_k x^k $$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "27b55cb2-60fb-4361-b581-c7891d85af71",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"\n"
],
"text/html": [
"
"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"using Plots\n",
"using Polynomials\n",
"default(lw=4, ms=5, legendfontsize=12, xtickfontsize=12, ytickfontsize=12)\n",
"\n",
"# Wilkinson's polynomial\n",
"n = 20\n",
"a = collect(1.:n)\n",
"w = fromroots(a)\n",
"w[10] *= 1 + 01 * 1e-10 # We can perturb coefficients\n",
"\n",
"# And plot it\n",
"plot(x -> abs(w(x)), xlims=(0, n+1), yscale=:log10, label=\"\\$w(x)\\$\")"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "54bbd78e-6597-49e5-b554-1fd31f8052bd",
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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",
"image/svg+xml": [
"\n",
"