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Homework_6

# Homework_6 - Homework 6 Due Wed Oct 11th Math 224 Fall 2011...

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Homework 6 - Due Wed. Oct. 11th Math 224 - Fall 2011 Dr. Mauro Maggioni Office hours : Tue 4-5, in office 293 Physics Bldg. Phone : 660-2825 Web page : www.math.duke.edu/˜ mauro E-mail : mauro.maggioni at duke.edu Homework policies : as in homework 1. All the materials (code, figures, etc...) have to be turned in (as printouts!) with your homework, or the homework will not be graded. Assignment Study Lectures 15,16 in the book. Exercises These exercises are taken/adapted from Heath’s book “Scientific Computing”: 1 . Write a program to compute the absolute and relative errors in Stirling’s approximation n ! 2 πn ( n/e ) n for n = 1 , . . . , 10. Does the absolute error grow or shrink as n increases? Does the relative error grow or shrink as n increases? 2 . In most floating-point systems, a quick approximation to the unit roundoff can be obtained by evaluating the expression ǫ machine ≈ | 3 * (4 / 3 - 1) - 1 | . (a) Explain why this trick works. (b) Try it in both double and single precision (if you are using Matlab, see help for single ).

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Homework_6 - Homework 6 Due Wed Oct 11th Math 224 Fall 2011...

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