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  "body": "\n## Summary\n\nSpline interpolation passes a [[spline|84TJ8KQ926]] through given data points, using the data nodes as knots.\nUnlike [[polynomial interpolation|SS1YMS2NPC]] of high degree, it keeps the degree of each piece low, which avoids [[Runge's phenomenon|ZMT8JF21R6]] and gives small errors for smooth data.\nThe most common choice is the [[cubic spline|V42H0R3EKX]], for which two extra conditions at the ends of the interval make the interpolant unique.\nThe coefficients solve a [[tridiagonal|DARX1KZRHZ]] linear system, so the cost grows only linearly with the number of points.\n\n## Explanations\n\n### L1 human\n\nConnecting data points by straight segments gives a curve with corners.\nSpline interpolation uses curved pieces instead, typically cubics, and chooses them so that neighbouring pieces meet with the same slope and the same bending.\nThe result looks like a smooth curve drawn through the points by hand.\nUnlike one polynomial through all the points, it does not swing wildly between the points when there are many of them.\nThe [[definition|RGT7WEZG8X]] states the conditions.\n",
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