lecture 2 measuring errors - Defined as the ratio between...

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1 Measuring Errors
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2 Why measure errors? 1) To determine the accuracy of numerical  results. 2) To develop stopping criteria for iterative  algorithms.
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3 True Error Defined as the difference between the true value in  a calculation and the approximate value found using  a numerical method etc. True Error = True (Exact) Value – Approximate Value
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4 Relative True Error Defined as the ratio between the true  error, and the true value. Relative True Error ( t ) =   True Error True Value
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5 Approximate Error What can be done if true values are not  known or are very difficult to obtain? Approximate error is defined as the  difference between the present  approximation and the previous  approximation. Approximate Error ( a E ) = Present Approximation – Previous Approximation 
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6 Relative Approximate Error
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Unformatted text preview: Defined as the ratio between the approximate error and the present approximation. Relative Approximate Error ( Approximate Error Present Approximation a ) = 7 How is Absolute Relative Error used as a stopping criterion? If s a | | where s is a pre-specified tolerance, then no further iterations are necessary and the process is stopped. If at least m significant digits are required to be correct in the final answer, then % 10 5 . | | 2 m a- 8 Table of Values For x e x f 5 . 7 ) ( = at 2 = x with varying step size, h 0.3 10.263 N/A 0.15 9.8800 0.038765% 3 0.10 9.7558 0.012731% 3 0.01 9.5378 0.024953% 3 0.001 9.5164 0.002248% 4 h ) 2 ( f a m THE END http://numericalmethods.eng.usf.edu...
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This note was uploaded on 08/11/2011 for the course MATH 663 taught by Professor Ron during the Spring '11 term at University of the Philippines Diliman.

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lecture 2 measuring errors - Defined as the ratio between...

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