Civil and Environmental Engineering 2219A/B Lecture 12: Roundoff and Truncation Errors

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Civil and Environmental Engineering
Civil and Environmental Engineering 2219A/B
Martha Dagnew

Lecture 12: Roundoff and Truncation Errors Accuracy and Precision Accuracy how closely a computed or measured value agrees with the true value Precision how closely individual computed or measured values agree with each other Error In iterative processes, error is approximated as the relative difference between successive iterations Types of Errors: o Roundoff Computers limited ability to store numbers Certain numerical manipulations highly sensitive to roundoff Large computations errors build up Smearing individual terms of summation larger than summation itself o Truncation Result from using approximation rather than exact mathematical procedure Example: Taylor series Total numerical error: o Summation of roundoff and truncation error o Truncation error increases as step size increases o Roundoff error decreases as step size increases Other important errors: o Blunders caused by computer malfunction or human error o Model errors incomplete mathematical models o Data uncertainty result from accuracy and precision of the data
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