USS Yorktown (1998) - I crewman accidentally entered a zero value as an input into the ship’s computer system. There was no validity check on the input data, and the result was a divide by zero which caused a cascade effect which lead to the total shutdown of the ship’s propulsion system for 2 hours and 45 minutes. This underscores the need to check for valid input in numerical calculations, which is similar to checking pre-conditions for calculations like proper interval brackets in bisection method where f(a)*f(b)<0, and dividing by zero or near zero in Newton’s and secant method which would cause divergence.

Millennium Bridge (2000) - When the stress analysis for the bridge was performed the 2Hz vertical wobbling was taken into account, but the 1Hz horizontal due to the wind was unaccounted for. This slight wobbling caused all of the pedestrians to walk in step, amplifying their vertical force causing a more intense wobbling of the bridge. This error came from an incomplete analysis of all the variables and conditions. Again pointing out the need to look at the entire situation before trusting your numerical calculations. The bridge reopened in 2002 after dampeners were installed to counteract the horizontal vibrations.

Patriot Missle (1991) - The patriot missle is an anti-missle defense missle to target incoming missles and take them out before they reach their target. It had an integer time value represeting the number 1/10ths of a second past when the missle system was initialized. When the time was later computed this integer representation was multiplied by a 24-bit floating point representation of .1 which had a truncation error of approximately 0.000000095. When the patriot missle system was running for 100 hours the total error was approximately .34 seconds, which is significant due to the fact that the missle travels at 1,676 meters per second. This error resulted in the patriot missle’s failure to take out an incoming Iraqi scud missle that caused 28 soldiers to die and another 100 to be injured. This error actually grows based on the amount of timefor which the system is running. The key takeaway here is to know how your truncation and rounding errors effect your final result and take them into account. Although I do not know what the official solution to this problem was, one solution would be the way we handle our error in the number of days in a year by adding February 29th every 4th year. A similar system could be employed in the patriot missile system after the error grew to a certain size.

http://books.google.com/books?id=JLKdVLjnCUwC&pg=PA10&lpg=PA10&dq=Vancouver+Stock+Exchange+truncation&source=web&ots=QXgGyVT5j9&sig=abtYZWczRJHTSwGecJgTqagtXx0&hl=en#PPA12,M1

http://www.ima.umn.edu/~arnold/disasters/patriot.html

http://ta.twi.tudelft.nl/nw/users/vuik/wi211/disasters.html