Lecture+11--Errors+_+floating+point+number

Lecture+11--Errors+_+floating+point+number - Disasters...

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Unformatted text preview: Disasters Caused by Comp. Arithmetic Error The Gulf War Patriot Missile Failure Patriot missile had an on-board timer that incremented every tenth of a second Software accumulated a floating point time value by adding 0.1 seconds Problem: 0.1 in floating point is NOT exactly 0.1 . With a 23 bit representation it is really only 0.0999999046326 => Error = 9.53674E-8 sec. Thus, after 100 hours ( 3,600,000 ticks), the software timer was off by 0.3433 seconds . Scud missile travels at 1676 m/s . In 0.3433 seconds , the Scud was 573 m away from where the Patriot thought it was. Far enough that the incoming Scud was outside the "range gate" that Patriot tracked. 2/25, 1991, an American Patriot Missile battery in Dharan, Saudi Arabia, failed to track and intercept an incoming Iraqi Scud missile. The Scud struck an American Army barracks, killing 28 soldiers and injuring around 100 other people. Taylor Series Expansion Used in constructing finite-difference formula Affects numerical accuracy => discretization error a x Base point x = a 2 3 1 2 3 ( ) ( ) ( ) ( ) ( ) o o f c c c c a a c f a x x x x a = +- +- +- + = L 2 1 2 3 1 ( ) 2 ( ) 3 ( ) ( ) f x c c x a c x a c f a = +- +- + = L 2 3 2 ( ) 2 6 ( ) ( ) / 2! f x c c x a c f a = +- + = L 3 3 ( ) 6 ( ) / 3! f x c c f a = + = L ( ) ( ) 1 ( ) ( !) ( 1) ( 1) 2 ( ) ( ) / ! m m m m o m f x m c m m m c x x c f a m + = + +-- + = M L L ( ) ( ) ( ) ( ) ( ) ! m m m m m m f a f c a a x x m x = = =- =- Taylor Series Expansion-0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 2 4 6 8 10 12 True Zero order 1 s t o r d e r-0.1 0.1 0.2 0.3 0.4 0.50....
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This note was uploaded on 11/07/2011 for the course EGM 3344 taught by Professor Raphaelhaftka during the Spring '09 term at University of Florida.

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Lecture+11--Errors+_+floating+point+number - Disasters...

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