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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 . . . . . . . . . . . . . . . . . . Condition of a Mathematical Problem . . . . . . . . . . . . . . . Stability of a Numerical Algorithm . . . . . . . . . . . . . . . . . 232 Root INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Four Algorithms for Root Finding . . . . . . . . . . . . . . . . . Bisection Method.

and the computational or floating-point representation xˆ = fl(x). Since infinite precision cannot be achieved with finite resources, the computational representation is a finite precision approximation of the exact value. Consider, for example, the decimal number x = 0.00012345876543.

  Computational

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