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Lecture 6 Notes

# 01 x within 1 of true value avoids unnecessary and

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Unformatted text preview: (# opera3ons) Bounds For |x- x*|<(Bn- An)/2 = En •  Rela3ve error: |x- x*|/|x| Gives accuracy of x* rela3ve to size of true value Generally not known since it depends on true value Bounds For |x- x*|<(Bn- An)/2 = En •  Rela3ve error: |x- x*|/|x| Gives accuracy of x* rela3ve to size of true value Generally not known since it depends on true value •  Rela3ve Error Bound: |x- x*|/|x| < En/(|x*|- En) Available when An<x<Bn away from zero Gives worst case rela3ve error As Bn- An - > 0, rela3ve error also goes to zero Bounds Given bounds for true value x, An < x < Bn Approximate x using x* = (An+Bn)/2 •  Absolute Error: |x- x*| Generally not know since it depends on true value •  Absolute Error Bound: |x- x*| < (Bn- An)/2 Always available gives worst case accuracy of x* As Bn- An - > 0, x* becomes more accu...
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