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

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Homework 5 Foundations of Computational Math 1 Fall 2010 The solutions will be posted on Wednesday, 10/13/10 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

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## This note was uploaded on 07/25/2011 for the course MAD 5403 taught by Professor Gallivan during the Spring '11 term at University of Florida.

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

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