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Spline Interpolation Method

Spline Interpolation Method. Industrial Engineering Majors Authors: Autar Kaw, Jai Paul http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates. Spline Method of Interpolation http://numericalmethods.eng.usf.edu. What is Interpolation ?.

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Spline Interpolation Method

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  1. Spline Interpolation Method Industrial Engineering Majors Authors: Autar Kaw, Jai Paul http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates http://numericalmethods.eng.usf.edu

  2. Spline Method of Interpolationhttp://numericalmethods.eng.usf.edu

  3. What is Interpolation ? Given (x0,y0), (x1,y1), …… (xn,yn), find the value of ‘y’ at a value of ‘x’ that is not given. http://numericalmethods.eng.usf.edu

  4. Interpolants Polynomials are the most common choice of interpolants because they are easy to: • Evaluate • Differentiate, and • Integrate. http://numericalmethods.eng.usf.edu

  5. Why Splines ? http://numericalmethods.eng.usf.edu

  6. Why Splines ? Figure : Higher order polynomial interpolation is a bad idea http://numericalmethods.eng.usf.edu

  7. Linear Interpolation http://numericalmethods.eng.usf.edu

  8. Linear Interpolation (contd) http://numericalmethods.eng.usf.edu

  9. 4 3 5 2 6 Y 1 X 7 Example A curve needs to be fit through the given points to fabricate the cam. If the cam follows a straight line profile between x = 1.28 to x = 0.66, what is the value of y at x=1.1 ? Find using linear spline interpolation. http://numericalmethods.eng.usf.edu

  10. Linear Interpolation http://numericalmethods.eng.usf.edu

  11. Linear Interpolation Find the cam profile using linear splines. http://numericalmethods.eng.usf.edu

  12. Linear Interpolation http://numericalmethods.eng.usf.edu

  13. Quadratic Interpolation http://numericalmethods.eng.usf.edu

  14. Quadratic Interpolation (contd) http://numericalmethods.eng.usf.edu

  15. Quadratic Splines (contd) http://numericalmethods.eng.usf.edu

  16. Quadratic Splines (contd) http://numericalmethods.eng.usf.edu

  17. Quadratic Splines (contd) http://numericalmethods.eng.usf.edu

  18. 4 3 5 2 6 Y 1 X 7 Example A curve needs to be fit through the given points to fabricate the cam. If the cam follows a straight line profile between x = 1.28 to x = 0.66, what is the value of y at x=1.1 ? Find using a quadratic spline interpolation. http://numericalmethods.eng.usf.edu

  19. Solution http://numericalmethods.eng.usf.edu

  20. Solution (contd) http://numericalmethods.eng.usf.edu

  21. Solution (contd) http://numericalmethods.eng.usf.edu

  22. Solution (contd) http://numericalmethods.eng.usf.edu

  23. Solution (contd) http://numericalmethods.eng.usf.edu

  24. Solution (contd) http://numericalmethods.eng.usf.edu

  25. Comparison http://numericalmethods.eng.usf.edu

  26. Additional Resources For all resources on this topic such as digital audiovisual lectures, primers, textbook chapters, multiple-choice tests, worksheets in MATLAB, MATHEMATICA, MathCad and MAPLE, blogs, related physical problems, please visit http://numericalmethods.eng.usf.edu/topics/spline_method.html

  27. THE END http://numericalmethods.eng.usf.edu

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