Transcription of INTRODUCTION TO COMPUTATIONAL MATHEMATICS
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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 .. Fixed Point Iteration .. Newton s Method .. Secant Method .. Stopping Criteria for Iterative Functions .. Rate of Convergence .. Convergence Theory .. Fixed Point Iteration .. Newton s Method.
cal operations (for example, addition, subtraction, multiplication and division) combined with flow constructs (if statements and loops). As such, even simple problems such as evaluating the exponential function may be difficult compu-tationally. Example 1.1 Consider the problem Pdefined by the evaluation of the exponen-tial function z = exp(x).
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