{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "YWTXGDC427"
    },
    {
      "field": "uses",
      "target": "ZMT8JF21R6"
    }
  ],
  "body": "\n## Summary\n\nChebyshev nodes are the zeros of a [[Chebyshev polynomial|M6EAR1JHPP]], possibly moved to an interval $[a, b]$ by an affine map.\nThey crowd near the ends of the interval.\nThey are the standard choice of points for [[polynomial interpolation|SS1YMS2NPC]], because they avoid the large errors that equally spaced points cause.\n\n## Explanations\n\n### L1 human\n\nTake points spaced evenly around the upper half of a circle and drop them straight down onto the diameter.\nThe shadows are the Chebyshev nodes: sparse in the middle and dense near the two ends.\nFor $n = 2$ the nodes in $[-1, 1]$ are $\\pm 1/\\sqrt{2}$, about $\\pm 0.707$.\nInterpolating at these points keeps the polynomial under control near the ends, where equally spaced points let it oscillate wildly.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "65D05",
      "41A05",
      "33C45"
    ],
    "name": "Chebyshev nodes",
    "same_as": {
      "wikidata": "Q1052508",
      "wikipedia": "Chebyshev nodes"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Chebyshev_nodes"
      }
    ],
    "tag": "HYK8J56PSH"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/HYK8J56PSH/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/HYK8J56PSH.md",
  "msc": [
    "65D05",
    "41A05",
    "33C45"
  ],
  "name": "Chebyshev nodes",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/HYK/HYK8J56PSH.md",
  "status": null,
  "tag": "HYK8J56PSH",
  "uri": "m2://HYK8J56PSH",
  "url": "https://tamnd.github.io/math2/wiki/chebyshev-nodes/",
  "writing": {
    "tag": "HYK8J56PSH",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}