Error bounds with approximated M value

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SUMMARY

The discussion focuses on approximating the value 'M' for the error bound formula in the Trapezoid Rule when the second derivative of a function is not available. Participants explore methods to estimate 'M' specifically for the error function (erf) to achieve an approximation within an error of 0.001. The conversation highlights the importance of understanding the error bound formula and the relationship between the function and its derivatives. Key resources include the error function and its properties, which are essential for accurate approximation.

PREREQUISITES
  • Understanding of the Trapezoid Rule in numerical integration
  • Familiarity with the error bound formula for numerical methods
  • Knowledge of the error function (erf) and its properties
  • Basic calculus concepts, particularly derivatives
NEXT STEPS
  • Research methods for estimating 'M' when derivatives are unavailable
  • Study the properties of the error function (erf) in detail
  • Learn about numerical integration techniques beyond the Trapezoid Rule
  • Explore advanced error analysis in numerical methods
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Mathematicians, students in numerical analysis, and anyone involved in computational mathematics seeking to improve their understanding of error bounds in numerical integration methods.

elemental_d
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How do you approximate the value 'M' for the error bound formula for the Trapezoid Rule of a function that the derivative cannot be found?

Error Bound Formula: http://archives.math.utk.edu/visual.calculus/4/approx.2/index.html

I'm trying to figure out the value of n to get erf(1.00) approximated within the error of 0.001?

Error Function: http://en.wikipedia.org/wiki/Error_function

How do i get M(in the error bound formula) when it is not possible to get the second derivative of the error function?
 
Physics news on Phys.org
But it IS possible to get the second derivative of erf.
 

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