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mws_gen_aae_spe_pptmeasuringerrors(1)

mws_gen_aae_spe_pptmeasuringerrors(1) - Measuring Errors...

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1/11/2010 http://numericalmethods.eng.usf.edu 1 Measuring Errors Major: All Engineering Majors Authors: Autar Kaw, Luke Snyder http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates
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Measuring Errors http://numericalmethods.eng.usf.edu
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http://numericalmethods.eng.usf.edu 3 Why measure errors? 1) To determine the accuracy of numerical results. 2) To develop stopping criteria for iterative algorithms.
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http://numericalmethods.eng.usf.edu 4 True Error Defined as the difference between the true value in a calculation and the approximate value found using a numerical method etc. True Error = True Value – Approximate Value
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http://numericalmethods.eng.usf.edu 5 Example—True Error The derivative, ) ( x f of a function ) ( x f can be approximated by the equation, h x f h x f x f ) ( ) ( ) ( ' + If x e x f 5 . 0 7 ) ( = and 3 . 0 = h a) Find the approximate value of ) 2 ( ' f b) True value of ) 2 ( ' f c) True error for part (a)
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http://numericalmethods.eng.usf.edu 6 Example (cont.) Solution: a) For 2 = x and 3 . 0 = h 3 . 0 ) 2 ( ) 3 . 0 2 ( ) 2 ( ' f f f + 3 . 0 ) 2 ( ) 3 . 2 ( f f = 3 . 0 7 7 ) 2 ( 5 . 0 ) 3 . 2 ( 5 . 0
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