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Newton’s Divided Difference Polynomial Method of Interpolation

Newton’s Divided Difference Polynomial Method of Interpolation. Civil Engineering Majors Authors: Autar Kaw, Jai Paul http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates.

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Newton’s Divided Difference Polynomial Method of Interpolation

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  1. Newton’s Divided Difference Polynomial Method of Interpolation Civil 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. Newton’s Divided Difference 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. Newton’s Divided Difference Method Linear interpolation: Given pass a linear interpolant through the data where http://numericalmethods.eng.usf.edu

  6. Example To maximize a catch of bass in a lake, it is suggested to throw the line to the depth of the thermocline. The characteristic feature of this area is the sudden change in temperature. We are given the temperature vs. depth plot for a lake. Determine the value of the temperature at z = −7.5 using Newton’s Divided Difference method for linear interpolation. Temperature vs. depth of a lake http://numericalmethods.eng.usf.edu

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

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

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

  10. Example To maximize a catch of bass in a lake, it is suggested to throw the line to the depth of the thermocline. The characteristic feature of this area is the sudden change in temperature. We are given the temperature vs. depth plot for a lake. Determine the value of the temperature at z = −7.5 using Newton’s Divided Difference method for quadratic interpolation. Temperature vs. depth of a lake http://numericalmethods.eng.usf.edu

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

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

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

  14. General Form where Rewriting http://numericalmethods.eng.usf.edu

  15. General Form http://numericalmethods.eng.usf.edu

  16. General form http://numericalmethods.eng.usf.edu

  17. Example To maximize a catch of bass in a lake, it is suggested to throw the line to the depth of the thermocline. The characteristic feature of this area is the sudden change in temperature. We are given the temperature vs. depth plot for a lake. Determine the value of the temperature at z = −7.5 using Newton’s Divided Difference method for cubic interpolation. Temperature vs. depth of a lake http://numericalmethods.eng.usf.edu

  18. Example http://numericalmethods.eng.usf.edu

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

  20. Example http://numericalmethods.eng.usf.edu

  21. Comparison Table http://numericalmethods.eng.usf.edu

  22. Thermocline What is the value of depth at which the thermocline exists? The position where the thermocline exists is given where . http://numericalmethods.eng.usf.edu

  23. 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/newton_divided_difference_method.html

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

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