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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 .. Secant Method .. Overview .. 443 Polynomial Interpolation .. The Vandermonde Matrix .. Lagrange Form.

Introduction to Computational Mathematics The goal of computational mathematics, put simply, is to find or develop algo-rithms that solve mathematical …

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