Lecture11

# Lecture11 - 3.25/1.96 = 1.65816326530162(from MATLAB But in...

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Unformatted text preview: 3.25/1.96 = 1.65816326530162... (from MATLAB) But in practice only report 1.65 (chopping) or 1.66 (rounding)! Why?? Because we don’t know what is beyond the 2 nd decimal place; so it could be False Significant Figures 4999 50 5 5 50 4999 5 5 3.25 .../1.96 1.6632602... 3.25 /1.96 ... 1.6497545... 3.25 .../1.95 ~ 3.25 /1.95 1.66496... 3.24 /1.96 ... ~ 3.24 /1.96 1. 999 9 65140... 99 Chopping Rounding = = = = Accuracy vs Precision ❧ Accuracy - How closely a measured or computed value agrees with the true value ❧ Precision - How closely individual measured or computed values agree with each other ❧ Accuracy is getting all your shots near the target. ❧ Precision is getting them close together. Accuracy and precision More Accurate More Precise Approximation = true value + true error E t = true value - approximation = x* - x or in percent * * x x x Value True Error True Error elative R- = = % * 100 * x x x t ×- = ε Numerical Errors The difference between the true value and the approximation %...
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Lecture11 - 3.25/1.96 = 1.65816326530162(from MATLAB But in...

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