MATH221 · Chapter 3 · Annotated SlidesInterpolation and the Lagrange Polynomial
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Interpolation and the Lagrange Polynomial

Interpolation and the Lagrange interpolating polynomial, its error formula, and worked examples.

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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 14 slides
  1. 1 Slide 1
  2. 2 Lagrange Interpolating Polynomials
  3. 3 Lagrange Interpolating Polynomials
  4. 4 Example 1
  5. 5 Slide 5
  6. 6 Slide 6
  7. 7 Example 2
  8. 8 Solution
  9. 9 Slide 9
  10. 10 Exercise Set 3.1
  11. 11 Slide 11
  12. 12 Exercise
  13. 13 Slide 13
  14. 14 Slide 14
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Slide 1

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Lagrange Interpolating Polynomials

Slide 2: Lagrange Interpolating Polynomials

Notes

  1. Error: f(x) − P(x) = f⁽ⁿ⁺¹⁾(ξ)/(n + 1)! · Π(x − xᵢ).

Exam angle

PredictionQ1

Find the linear Lagrange polynomial through (2, 4) and (5, 1).

Compare with the model answer

P(x) = 4(x − 5)/(2 − 5) + 1(x − 2)/(5 − 2) = −(4/3)(x − 5) + (1/3)(x − 2) = −x + 6.

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Lagrange Interpolating Polynomials

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Example 1

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Example 2

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Solution

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Exercise Set 3.1

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Exercise

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