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mws_gen_inp_ppt_direct(1)

# mws_gen_inp_ppt_direct(1) - Direct Method of Interpolation...

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http://numericalmethods.eng.usf.edu 1 Direct Method of Interpolation 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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Direct Method of Interpolation http://numericalmethods.eng.usf.edu
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. Figure 1 Interpolation of discrete.

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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
http://numericalmethods.eng.usf.edu 5 Direct Method Given ‘n+1’ data points (x 0 ,y 0 ), (x 1 ,y 1 ),…………. . (x n ,y n ), pass a polynomial of order ‘n’ through the data as given below: where a 0 , a 1 ,………………. a n are real constants. Set up ‘n+1’ equations to find ‘n+1’ constants. To find the value ‘y’ at a given value of ‘x’, simply substitute the value of ‘x’ in the above polynomial. . .......... .......... 1 0 n n x a x a a y + + + =

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http://numericalmethods.eng.usf.edu 6 Example 1 The upward velocity of a rocket is given as a function of time in Table 1. Find the velocity at t=16 seconds using the direct method for linear interpolation. 0 0 10
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mws_gen_inp_ppt_direct(1) - Direct Method of Interpolation...

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