{
  "aliases": null,
  "backlinks": [
    {
      "field": "specializes",
      "target": "237KR6FRCK"
    },
    {
      "field": "defines",
      "target": "EKDSDN89FR"
    },
    {
      "field": "uses",
      "target": "M0HC35HZ5H"
    },
    {
      "field": "uses",
      "target": "QGQTYT6YZR"
    },
    {
      "field": "uses",
      "target": "TEQNAME853"
    }
  ],
  "body": "\n## Summary\n\nPolynomial interpolation finds a polynomial whose graph passes through finitely many given points.\nThrough $n + 1$ points with distinct first coordinates there is exactly one polynomial of degree at most $n$.\n[[Lagrange interpolation|237KR6FRCK]] gives an explicit formula for it.\nIt is a basic tool to approximate functions, to derive numerical integration rules and to reconstruct polynomials from their values.\n\n## Explanations\n\n### L1 human\n\nThrough two points there is one line, and through three points with distinct $x$-values there is one parabola or line.\nIn general, $n + 1$ points fix a polynomial of degree at most $n$.\nFor the points $(0, 1)$, $(1, 3)$ and $(2, 7)$ the polynomial is $x^2 + x + 1$.\nThe [[definition|EKDSDN89FR]] states the conditions.\n",
  "commit": "547b6eddb8f2feb8d579f2d633d22a27b7e132fc",
  "front": {
    "kind": "concept",
    "msc": [
      "41A05",
      "65D05"
    ],
    "name": "Polynomial interpolation",
    "same_as": {
      "wikidata": "Q637347",
      "wikipedia": "Polynomial interpolation"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Polynomial_interpolation"
      }
    ],
    "tag": "SS1YMS2NPC"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/SS1YMS2NPC/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/SS1YMS2NPC.md",
  "msc": [
    "41A05",
    "65D05"
  ],
  "name": "Polynomial interpolation",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/SS1/SS1YMS2NPC.md",
  "status": null,
  "tag": "SS1YMS2NPC",
  "uri": "m2://SS1YMS2NPC",
  "url": "https://math2.tamnd.com/wiki/polynomial-interpolation/",
  "writing": {
    "tag": "SS1YMS2NPC",
    "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
      }
    ]
  }
}