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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 .. Bisection Method.

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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