CS335 Study Guide - Final Guide: Truncation Error, Condition Number, Round-Off Error

• School: University of Waterloo
• Department: Computer Science
• Course: CS335
• Professor: Zhiyong Liu

Document Summary

There are several sources of error in solving real-world scienti c computing problems. Some errors occur before a computation begins: modeling error: some features simpli ed or omitted, data error: measurement errors, lack of data, error from previous computations. 1. 2 absolute error and relative error: absolute error : approximate value - true value, relative error: absolute error true value, the relative error is usually a more meaningful measure than absolute error. Note: true value usually unknown, so we estimate or bound error rather than compute it exactly. However, we have: input x instead of input x, approximate function f (x) rather than true f (x), in general, you can think f as the exact algorithm, while f is an approximate algorithm. Total error: f ( x) f (x) = ( f ( x) f ( x)) {z computational error (f ( x) f (x)) Example: let f (x) = sin(x), and we want to approximate sin( /8).