INTRODUCTION TO COMPUTATIONAL MATHEMATICS
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.
Mathematics The goal of computational mathematics, put simply, is to find or develop algo-rithms that solve mathematical problems computationally (ie. using comput-ers). In particular, we desire that any algorithm we develop fulfills four primary properties: • Accuracy. An accurate algorithm is able to return a …
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