mws_gen_inp_ppt_spline(1) - Spline Interpolation Method...

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http://numericalmethods.eng.usf.edu 1 Spline Interpolation Method Major: All Engineering Majors Authors: Autar Kaw, Jai Paul http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates
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Spline Method of Interpolation http://numericalmethods.eng.usf.edu
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http://numericalmethods.eng.usf.edu 3 What is Interpolation ? Given (x 0 ,y 0 ), (x 1 ,y 1 ), …… (x n ,y n ), find the value of ‘y’ at a value of ‘x’ that is not given.
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http://numericalmethods.eng.usf.edu 4 Interpolants Polynomials are the most common choice of interpolants because they are easy to: Evaluate Differentiate, and Integrate .
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http://numericalmethods.eng.usf.edu 5 Why Splines ? 2 25 1 1 ) ( x x f + = Table : Six equidistantly spaced points in [-1, 1] Figure : 5 th order polynomial vs. exact function x 2 25 1 1 x y + = -1.0 0.038461 -0.6 0.1 -0.2 0.5 0.2 0.5 0.6 0.1 1.0 0.038461
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