Lecture+12--Errors

# Lecture+12--Errors - Disasters Caused by Comp Arithmetic...

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Disasters Caused by Comp. Arithmetic Error On June 4, 1996, an unmanned Ariane 5 rocket was launched. The rocket was on course for 36 seconds and then veered off and crashed The internal reference system was trying to convert a 64-bit floating point number to a 16-bit integer . This caused an overflow which was sent to the onboard computer. The on-board computer interpreted the overflow as real flight data and bad things happened. The destroyed rocket and its cargo were valued at \$500 million. The rocket was on its first voyage, after a decade of development costing \$7 billion. Ariane Rocket disaster

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Machine precision or machine epsilon ε The smallest number for which fl (1 + ε ) > 1; fl ”=floating point operation For any x< , we have fl (1 + x) = 1 In Excel : = 1.7764E-15 n x= 1/2^n y=1+x y-1 45 2.8422E-14 1.0000000000000 300 2.8422E-14 46 1.4211E-14 1.0000000000000 100 1.4211E-14 47 7.1054E-15 1.0000000000000 100 7.1054E-15 48 3.5527E-15 1.0000000000000000 3.5527E-15 49 1.7764E-15 1.0000000000000000 1.7764E-15 50 8.8818E-16 1.0000000000000000 0.0000E+00 51 4.4409E-16 1.0000000000000000 0.0000E+00
Matlab Environment Double precision (64 bits)

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Lecture+12--Errors - Disasters Caused by Comp Arithmetic...

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