N12 - ME 510 NUMERICAL METHODS FOR ME II Norms Given: A...

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ME – 510 NUMERICAL METHODS FOR ME II gG±²³´µG³´¶·G¸¹´ºG»¼½ Fall 2007 Norms Given : A function, f (x), or tabulated data points in a certain range, [a , b] Problem: A simple function, g(x), that represents or fits the given f (x) or the data points in [a , b] according to a certain "goodness" or "closeness" is required. How do we define "goodness" of fitting? Answer: There are basically three ways of defining "goodness" which are called "Norms" ME – 510 NUMERICAL METHODS FOR ME II gG±²³´µG³´¶·G¸¹´ºG»¼½ Fall 2007 Chebyshev, or L g Norm : Minimize maximum error, i.e., Max. g f (x) - g (x) g in [a , b] Least Deviation or L 1 Norm : Minimize average error, i.e., Least Squares or L 2 Norm : Minimize sum of the squares of the error, i.e. dx (x) g - (x) f b a g G ± dx (x) g - (x) f b a 2 g
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ME – 510 NUMERICAL METHODS FOR ME II
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This note was uploaded on 02/28/2011 for the course ME 510 taught by Professor Dr.faruckarinc during the Spring '11 term at Middle East Technical University.

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N12 - ME 510 NUMERICAL METHODS FOR ME II Norms Given: A...

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