Absolute relative approximate error

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SUMMARY

The discussion centers on the concept of "absolute relative approximate error," specifically its calculation in iterative methods. The formula provided for this error is ((x_present - x_previous) / x_present) * 100, where x_present is the current approximation and x_previous is the previous approximation. The importance of using an approximate value instead of an exact value for determining relative error is emphasized, as the exact value is often unknown in practical scenarios.

PREREQUISITES
  • Understanding of numerical methods and iterative algorithms
  • Familiarity with error analysis in computational mathematics
  • Basic knowledge of absolute and relative error concepts
  • Proficiency in mathematical notation and formulas
NEXT STEPS
  • Study numerical methods for root-finding, such as Newton's method
  • Learn about error analysis techniques in numerical computations
  • Explore the concept of convergence in iterative algorithms
  • Investigate the implications of approximation errors in engineering applications
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This discussion is beneficial for students and professionals in fields such as mathematics, engineering, and computer science, particularly those involved in numerical analysis and algorithm development.

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I'm a bit confused, i have a question, it asks me to find ''the absolute relative approximate error'' at the end of each iteration. What's the formula of ''the absolute relative approximate error''?
 
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absolute means the size of the error (ie. the absolute value of the error), and relative means relative to the exact value. So the formula would be (absolute value of the error)/(exact value).
 
The exact value is presumably unknown. Why go to the effort of finding an approximate solution if you already know the exact value? The exact value cannot be used to determine the relative error. An approximate value is available, so that is the appropriate thing to use in computing the scaled (or relative) error. Hence the term "absolute relative approximate error".
 
I find lecture notes:

''the absolute relative approximate error'' = (( x_present - x_previous ) / x_present )*100
 

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