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Advanced Computer Programming: Interpolation Techniques Overview

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In this course, we explore key interpolation methods used in computational mathematics, focusing on quadratic, cubic, and spline interpolations. Students will learn how to apply these techniques through practical examples, including applications in chemical engineering. We will delve into how to construct polynomials that accurately fit given data points and evaluate complex functions. The course emphasizes construction simplicity and the ability to approximate intricate shapes via curve fitting, aiding in both theoretical understanding and practical implementation.

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Advanced Computer Programming: Interpolation Techniques Overview

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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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