MATH221 · Chapter 3 · Annotated SlidesCubic Spline Interpolation
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Cubic Spline Interpolation

Cubic spline interpolation: piecewise cubics with continuous first and second derivatives, natural vs. clamped boundary conditions, and solving for the coefficients.

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Every original slide is shown unchanged. Yellow marks on a slide point to a numbered note: hover or tap a mark to jump to its note, and hover a note to see its marks. Questions tagged Past exam appeared on a real paper; Prediction questions are likely angles, not confirmed. Pick an answer to each question: a wrong pick tells you why it is wrong, so you can try again.

All 22 slides
  1. 1 Slide 1
  2. 2 Slide 2
  3. 3 Slide 3
  4. 4 Natural Splines
  5. 5 Slide 5
  6. 6 Slide 6
  7. 7 Slide 7
  8. 8 Clamped
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  10. 10 Slide 10
  11. 11 Slide 11
  12. 12 Slide 12
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  16. 16 Slide 16
  17. 17 Slide 17
  18. 18 Slide 18
  19. 19 Slide 19
  20. 20 Slide 20
  21. 21 Slide 21
  22. 22 Slide 22
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Notes

  1. Cubic spline: Sⱼ(x) = aⱼ + bⱼ(x − xⱼ) + cⱼ(x − xⱼ)² + dⱼ(x − xⱼ)³ on each subinterval; S, S′, S″ continuous.

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Natural Splines

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Clamped

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Notes

  1. Clamped spline: S′(x₀) = f′(x₀), S′(xₙ) = f′(xₙ) (usually more accurate).

Exam angle

PredictionQ1

A natural cubic spline satisfies at the endpoints:

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