Lecture 6 Notes

Lecture 6 Notes

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Unformatted text preview: rate Rela3ve Error Very useful, e.g., when working with billions of dollars, don’t worry about pennies (or thousands or maybe even individual millions) |x- x*|/|x| < %p => x* correct within %p of true value |x- x*|/|x| < .01 => x* within 1% of true value Avoids unnecessary (and oyen irrelevant) computa3on Quiz Time How close is x* to x when x is on the order of one billion dollars, and the rela3ve error bound is less than 0.02? |x- x*|/|x| < En/(|x*|- En) < .02 => x* is within $Y of x? A) $2 B) $2 million C) $20 million D) $50 million Remark: En/(|x*|- En) = En/min(|An|,|Bn|) 3 2/11/14 Bounds General numerical approxima3on setup: |x- x*|< En •  Desired quan3ty x could be a constant, or something more general like a func3on •  Approxima3on x* and bound En can also be more general •  The Science finding “...
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This document was uploaded on 03/11/2014 for the course CSCI 004 at Brown.

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