Length_of_curve_experiment -...

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http://numericalmethods.eng.usf.edu/experiments Length of curve experiment Background: The motivation behind the experiment is Runge’s numerical experiment to show that higher order interpolation is a bad idea. Read these pages ( 1 , 2 ) of the book where it is shown that as you use higher order interpolants to approximate f ( x )=1/ (1+25 x 2 ) in [-1,1], the differences between the original function and the interpolants becomes worse. This concept also becomes the basis why we use splines rather than polynomial interpolation to find smooth paths to travel through several discrete points (Read these pages for further information). What you will do in the lab : A flexible curve (Figure 1) made of lead-core construction with inch graduations from 0 to 12" is provided to you. You need to draw a curve similar in shape to the Runge’s curve on the provided graphing paper as shown. It just needs to be similar in shape – you can make the x -domain shorter and the maximum y -value larger or vice-versa. Just be sure that there is only one value of
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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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Length_of_curve_experiment -...

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