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hw5 - Homework 5 Foundations of Computational Math 1 Fall...

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Homework 5 Foundations of Computational Math 1 Fall 2011 The solutions will be posted on Friday, 10/14/11 Problem 5.1 Consider the following numbers: 122.9572 457932 0.0014973 5.1.a . Express the numbers as floating point numbers with β = 10 and t = 4 using rounding to even and using chopping. 5.1.b . Express the numbers as floating point numbers with in single precision IEEE format using rounding to even. It is strongly recommended that you implement a program to do this rather than computing the representation manually. 5.1.c . Calculate the relative error for each number and verify it satisfies the bounds implied by the floating point system used. Problem 5.2 Consider the function f ( x ) = 1 . 01 + x 1 . 01 - x 5.2.a . Find the absolute condition number for f ( x ). 5.2.b . Find the relative condition number for f ( x ). 5.2.c . Evaluate the condition numbers around x = 1. 5.2.d . Check the predictions of the condition numbers by examining the relative error and the absolute error err rel = | f ( x 1 ) - f ( x 0 ) | | f ( x 0 ) | err abs = | f ( x 1 ) - f ( x 0 ) | with x 0 = 1, x 1 = x 0 (1 + δ ) and δ small.
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