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Propagation of Errors - Numerical Methods - Lecture Slides

Slides, Numerical Methods

Post: April 17th, 2013
Description
The main points are: Propagation of Errors, Numerical Methods, Maximum Possible Value, Errors in Formulas, Axial Member, Formula for Error Propagation, Subtraction of Numbers, Objective Function, Vector Operator, Initial Guess of Root
The main points are: Propagation of Errors, Numerical Methods, Maximum Possible Value, Errors in Formulas, Axial Member, Formula for Error Propagation, Subtraction of Numbers, Objective Function, Vector Operator, Initial Guess of Root
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Propagation of Errors Docsity.com Propagation of Errors In numerical methods, the calculations are not made with exact numbers. How do these inaccuracies propagate through the calculations? Docsity.com Example 1: Find the bounds for the propagation in adding two numbers. For example if one is calculating X +Y where X = 1.5 ± 0.05 Y = 3.4 ± 0.04 Solution Maximum possible value of X = 1.55 and Y = 3.44 Maximum possible value of X + Y = 1.55 + 3.44 = 4.99 Minimum possible value of X = 1.45 and Y = 3.36. Minimum possible value of X + Y = 1.45 + 3.36 = 4.81 Hence 4.81 ≤ X + Y ≤4.99. Docsity.com Propagation of Errors In Formulas If f is a function of several variables X 1 , X 2 , X 3 ,......., X n −1 , X n then the maximum possible value of the error in f is ∂f ∂f ∂f ∂f ∆X n −1 + ∆X n ∆X 2 + ....... + ∆f ≈ ∆X 1 + ∂X n ∂X n −1 ∂X 1 ∂X 2 Docsity.com Example 2: The strain in an axial member of a square crosssection is given by Given F ∈= 2 ..

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