Homework #0
1. Suppose we have a computer that performs 3 digit rounding.
What absolute and
relative errors do you get for the following numbers and operations performed on that
computer:
(a) 8
.
1146
(b) 1004
.
21 + 2138
.
6
(c) 4
.
369
·
3
.
4
2. Consider a computer that performs 3 digit rounding for the following:
(a) Find an example of positive real numbers
a
and
b
such that the floating point
representation for
a

b
has an absolute error
≥
1000.
(b) Find an example of positive real numbers
c
and
d
such that the floating point
representation for
c

d
has a relative error that exists and is
≥
90%.
3. For the following, work with exact arithmetic:
(a) Suppose
x
= 1 but our approximation is
x
*
= 1
.
001. What are the absolute and
relative errors of 10
6
·
(
x

1
.
0005) when using the approximation?
(b) Suppose
x
= 1 but our approximation is
x
*
= 1
.
001. What is the absolute error
of the operation
∑
1000000
k
=1
x
when using the approximation?
(c) Suppose
x
= 1 but our approximation is
x
*
= 1
.
001. Will the relative error of the
operation
Q
n
k
=1
x
become
≥
1000 as
n
→ ∞
when using the approximation?
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 Spring '08
 staff
 Numerical Analysis, positive real numbers, floating point representation

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