1
COMPUTER SCIENCE 349A
Handout Number 2
Measures of error
(pages 54-57 of the 5
th
edition of the textbook; pages 56-59 of the 6
th
edition)
If
p
denotes the true (exact) value of some quantity, and
*
p
denotes some
approximation to
p
, then
*
p
p
E
t
−
=
is called the
absolute error
, and
p
p
p
p
p
t
*
1
*
−
=
−
=
ε
(if
0
≠
p
)
is called the
relative error
.
Absolute error
is not a meaningful measure of error unless you know the
magnitude of
p
, the quantity you are approximating.
For example,
if
1234000
*
and
1234321
=
=
p
p
, then
321
=
t
E
seems large, although
*
p
is
quite accurate and agrees with
p
to 4 significant digits;
if
001111
.
0
*
and
001234
.
0
=
=
p
p
, then
000123
.
0
=
t
E
seems small, although
*
p
is not very accurate and agrees with
p
to only 1 significant digit.
Relative error
, which is always meaningful, in fact indicates the number of
correct significant digits in an approximation
*
p
.
Example
Consider
L
14159265
.
3
=
=
π
p
000029
.
0
5
1415
.
3
00019
.
0
4
141
.
3
00051
.
0
3
14
.
3
013
.
0
2
1
.
3
error
relative
digits
t
significan
correct
of
number
to
*
ions
approximat
p
p

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