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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 Fall '09
 gallivan
 Numerical Analysis, floating point numbers

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