nbm_gen_inp_ppt_ndd - Interpolation Topic: Newtons Divided...

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http://numericalmethods.eng.usf.edu 1 Interpolation Topic: Newton’s Divided Difference Polynomial Method Major: General
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http://numericalmethods.eng.usf.edu 2 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 3 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 4 Newton’s Divided Difference Method Linear interpolation : Given pass a linear interpolant through the data where ), , ( 0 0 y x ), , ( 1 1 y x ) ( ) ( 0 1 0 1 x x b b x f + = ) ( 0 0 x f b = 0 1 0 1 1 ) ( ) ( x x x f x f b =
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http://numericalmethods.eng.usf.edu 5 Example 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 Newton Divided Difference method for linear interpolation. 901.67 30 602.97 22.5 517.35 20 362.78 15 227.04 10 0 0 m/s s v(t) t Table 1: Velocity as a function of time Figure 2: Velocity vs. time data for the rocket example
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http://numericalmethods.eng.usf.edu 6 Linear Interpolation 10 12 14 16 18 20 22 24 350 400 450 500 550 517.35 362.78 y s f range () fx desired x s 1 10 + x s 0 10 x s range , x desired , , 15 0 = t 78 . 362 ) ( 0 = t v , 20 1 = t 35 . 517 ) ( 1 = t v ) ( 0 0 t v b = 78 . 362 = 0 1 0 1 1 ) ( ) ( t t t v t v b = 914 . 30 = ) ( ) ( 0 1 0 t t b b t v + =
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http://numericalmethods.eng.usf.edu 7 Linear Interpolation (contd) 10 12 14 16 18 20 22 24 350 400 450 500 550 517.35 362.78 y s f range () fx desired x s 1 10 + x s 0 10 x s range , x desired , ) ( ) ( 0 1 0 t t b b t v + = ), 15 ( 914 . 30 78 . 362 + = t 20 15 t At 16 = t ) 15 16 ( 914 . 30 78 . 362 ) 16 ( + = v 69 . 393 = m/s
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http://numericalmethods.eng.usf.edu 8
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This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida.

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nbm_gen_inp_ppt_ndd - Interpolation Topic: Newtons Divided...

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