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KKKQ 3013 PENGIRAAN BERANGKA

KKKQ 3013 PENGIRAAN BERANGKA. Week 6 – Interpolation & Curve Fitting 14 August 2007 8.00 am – 9.00 am. Topics. .

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KKKQ 3013 PENGIRAAN BERANGKA

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  1. KKKQ 3013PENGIRAAN BERANGKA Week 6 – Interpolation & Curve Fitting 14 August 2007 8.00 am – 9.00 am

  2. Topics  􀂉 Introduction 􀂉 Newton Interpolation: Finite Divided Difference 􀂉 Lagrange Interpolation 􀂉 Spline Interpolation 􀂉 Polynomial Regression 􀂉 Multivariable Interpolation   Week 6

  3. Tutorial Example 1 (adapted courtesy of ref. [1]) From table 1 below, estimate f(x) at x = 5.5 using the third order (cubic) Newton interpolating polynomial. As a start, use points x = 1, 4, 5 & 6. [1] KQ3013 lecture notes Week 6

  4. Tutorial Example 1 (adapted courtesy of ref. [1]) The third order Newton interpolating polynomial, eq. (3.5) i.e. n = 3: [1] KQ3013 lecture notes Week 6

  5. Tutorial Example 1 (adapted courtesy of ref. [1]) where from equation (3.6c) [1] KQ3013 lecture notes Week 6

  6. Tutorial Example 1 (adapted courtesy of ref. [1]) Note for b3: [1] KQ3013 lecture notes Week 6

  7. Tutorial Example 1 (adapted courtesy of ref. [1]) The first divided difference: [1] KQ3013 lecture notes Week 6

  8. Tutorial Example 1 (adapted courtesy of ref. [1]) Therefore, the second divided difference: and hence, the third divided difference: [1] KQ3013 lecture notes Week 6

  9. Tutorial Example 1 (adapted courtesy of ref. [1]) Summarising the divided difference calculation: Therefore, 3rd order Newton polynomial: Now, repeat using points x = 4, 5, 6 & 7. Which group of points gives closer approximation to true value ? and ln 5.5 [1] KQ3013 lecture notes Week 6

  10. Tutorial Example 1 (adapted courtesy of ref. [1]) Summarising the divided difference calculation for next group of points: and ln 5.5 Exact or true value: ln 5.5 = 1.704748 !! Week 6

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