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lecture 3 sources of error - Sources of Error 1 Two sources...

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1 Sources of Error
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2 Two sources of numerical error 1) Round-off error 2) Truncation error
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3 Round off Error Caused by representing a number approximately ... 333333 . 0 3 1 2245 ... 4142 . 1 2 2245
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4 Problems created by round-off error Around 100 Americans were killed on February 25, 1991 by an Iraqi Scud missile in Dhahran, Saudi Arabia.
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5 Effect of Carrying Significant Digits in Calculations
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6 Thermal Expansion Coefficient vs Temperature T D D = α T( o F) α (μin/in/ o F) -340 2.45 -300 3.07 -220 4.08 -160 4.72 -80 5.43 0 6.00 40 6.24 80 6.47
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7 Regressing Data in Excel (general format) 0.00 4.00 8.00 -400 -200 0 200 T ( o F) Alpha ( in/in/ o F) α = -1E-05T 2 + 0.0062T + 6.0234
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8 Observed and Predicted Values T( o F) α (μin/in/ o F) Given α (μin/in/ o F) Predicted -340 2.45 2.76 -300 3.07 3.26 -220 4.08 4.18 -160 4.72 4.78 -80 5.43 5.46 0 6.00 6.02 40 6.24 6.26 80 6.47 6.46 α = -1E-05T 2 + 0.0062T + 6.0234
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9 Regressing Data in Excel (scientific format) 0.00 4.00 8.00 -400 -200 0 200 T ( o F) Alpha ( in/in/ o F) α = -1.2360E-05T 2 + 6.2714E-03T + 6.0234
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10 Observed and Predicted Values T( o F) α (μin/in/ o F) Given α (μin/in/ o F) Predicted -340 2.45 2.46 -300 3.07 3.03 -220 4.08 4.05 -160 4.72 4.70 -80 5.43 5.44 0 6.00 6.02 40 6.24 6.25 80 6.47 6.45 α = -1.2360E-05T 2 + 6.2714E-03T + 6.0234
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11 Observed and Predicted Values T( o F) α (μ in/in/ o F) Given
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12 THE END
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13 Truncation Error
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14 Truncation error Error caused by truncating or approximating a mathematical procedure.
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