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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.

point is 0 and the first digit right of the decimal point is nonzero). The number ˆx is thus normalized as follows: x = 0.12345876543|{z } mantissa ×10−3. (1.3) However, a computer can only represent finite precision, so we are not guaranteed …

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