1 / 10

KKKQ 3013 PENGIRAAN BERANGKA

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

gaerwn
Télécharger la présentation

KKKQ 3013 PENGIRAAN BERANGKA

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related