Transcription of Section 4 Roundoff and Truncation Error
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Section 4 Roundoff and Truncation Error
MAE 4020/5020 Numerical Methods with MATLABSECTION 4: Roundoff AND Truncation ERRORSD efinitions of Error2K. Webb MAE 4020/50203 True ErrorK. Webb MAE 4020/5020 Absolute Error the difference between an approximation and the true value Relative Error the true Error as a percentage of the true value Both definitions require knowledge of the true value! If we had that, why would we be approximating?4 Approximating the ErrorK. Webb MAE 4020/5020 Since we don t know the true value, we can only approximate the Error Often, approximations are made iteratively Approximate the Error as the change in the approximate value from one iteration to the next 5 Relative Approximate ErrorK. Webb MAE 4020/5020 We don t know the true value, so we can t calculate the true Error approximate the Error Relative approximate Error an approximation of the Error relative to the approximation itself 6 Stopping CriterionK. Webb MAE 4020/5020 For iterative approximations, continue to iterate until the relative approximate Error magnitude is less than a specified stopping criterion For accuracy to at least significant figures set the stopping criterion to Roundoff Error7K.
10 Binary Number System K. Webb MAE 4020/5020 Computers represent numbers in binaryformat A base‐2 number system Two digits: 0, 1 Easy to store binary values in computer hardware –an on or off switch –a high or low voltage One digit is a bit –eight bits is a byte Each bit represents an integer power of 2
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