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Computer Programming (TKK-2144)

13/14 Semester 1. Computer Programming (TKK-2144). Instructor: Rama Oktavian Email: rama.oktavian@ub.ac.id Office Hr.: M.13-15, W. 13-15 Th. 13-15, F. 13-15. Outlines. 1. Quadratic Interpolation. 2. Cubic Interpolation. 3 . Spline Interpolation . 4. Example in chem.eng.

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Computer Programming (TKK-2144)

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  1. 13/14 Semester 1 Computer Programming(TKK-2144) Instructor: Rama Oktavian Email: rama.oktavian@ub.ac.id Office Hr.: M.13-15, W. 13-15 Th. 13-15, F. 13-15

  2. Outlines 1. Quadratic Interpolation 2. Cubic Interpolation 3. Spline Interpolation 4. Example in chem.eng

  3. Quadratic interpolation We want to find a polynomial which satisfies for for given data points (x0,y0),(x1,y1),(x2,y2).

  4. Quadratic interpolation The upward velocity of a rocket is given as a function of time in Table 2. Find the velocity at t=16 seconds using the direct method for quadratic interpolation. Table 1 Velocity as a function of time. Figure 1Velocity vs. time data for the rocket example http://numericalmethods.eng.usf.edu 4

  5. Quadratic interpolation Figure 2 Quadratic interpolation. Solving the above three equations gives http://numericalmethods.eng.usf.edu

  6. Quadratic interpolation Figure 2Quadratic interpolation. http://numericalmethods.eng.usf.edu

  7. Cubic Interpolation Figure 3 Cubic interpolation. http://numericalmethods.eng.usf.edu

  8. Cubic Interpolation Figure 3 Cubic interpolation. http://numericalmethods.eng.usf.edu

  9. Spline Interpolation • Spline: • In Mathematics, a spline is a special function defined piecewise by polynomials; • In Computer Science, the term spline more frequently refers to a piecewise polynomial (parametric) curve. • Simple construction, ease and accuracy of evaluation, capacity to approximate complex shapes through curve fitting and interactive curve design.

  10. Spline Interpolation • Spline Interpolation: • Linear spline • Quadratic spline • Cubic spline

  11. Spline Interpolation • LinearSpline Interpolation:

  12. Spline Interpolation • LinearSpline Interpolation: http://numericalmethods.eng.usf.edu

  13. Spline Interpolation • QuadraticSpline Interpolation: http://numericalmethods.eng.usf.edu

  14. Spline Interpolation • QuadraticSpline Interpolation: http://numericalmethods.eng.usf.edu

  15. Spline Interpolation • QuadraticSpline Interpolation: http://numericalmethods.eng.usf.edu

  16. Thank You !

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