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INTRODUCTION TO COMPUTATIONAL MATHEMATICS

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INTRODUCTION TOCOMPUTATIONALMATHEMATICSCourse Notes forCM 271 / AM 341 / CS 371H. De SterckP. UllrichDepartment of Applied MathematicsUniversity of WaterlooMarch 20th, 2006These notes have been funded by2Contents1 Errors and Error Sources of Error . . . . . . . . . . . . . . . . . . . . . . . . . . . Floating Point Numbers and Operations . . . . . . . . . . . . . . A Binary Computer . . . . . . . . . . . . . . . . . . . . . Standard floating point systems . . . . . . . . . . . . . . . Machine Precision . . . . . . . . . . . . . . . . . . . . . . Floating Point Operations.

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) …

  Calculating

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