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INTRODUCTION TO COMPUTATIONAL MATHEMATICS

INTRODUCTION TOCOMPUTATIONALMATHEMATICSC ourse Notes forCM 271 / AM 341 / CS 371H. De SterckP. UllrichDepartment of Applied MathematicsUniversity of WaterlooMarch 20th, 2006 These notes have been funded by2 Contents1 Errors and Error Sources of Error .. Floating Point Numbers and Operations .. A Binary Computer .. Standard floating point systems .. Machine Precision .. Floating Point Operations .. Condition of a Mathematical Problem .. Stability of a Numerical Algorithm .. 232 Root INTRODUCTION .. Four Algorithms for Root Finding.

calculating exp(−5.5) (see Table I), we see that there were several subtractions performed of numbers of similar magnitude. Fortunately, we have an easy way around this if we simply take advantage of a property of the exponential, namely exp(−x) …

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