Graphics Programs Reference
In-Depth Information
Where
p
i
is the population for year
x
i
, and
i
=1
,
2
,...N
. We can write
this series of equations as a matrix equation:
x
1
p
1
p
2
.
.
.
p
N
1
x
1
c
0
c
1
c
2
1
x
2
x
2
.
=
.
.
.
1
x
N
x
2
N
Or, defining matrices,
P
=
X
·
C
.
In matlab the
X
matrix is calculated as follows:
>> X = [ones(size(year)) year year.^2]
X=
1
1788
3196944
1
1790
3204100
.
.
.
1
1993
3972049
1
1994
3976036
1
1995
3980025
The backslash operator solves the equation for the coeQcient matrix
C
:
>> C = X\P
C=
1.0e+09 *
2.0067
-0.0022
0.0000
The third coe
Q
cient is not really zero; it is simply too small (compared
to 2
.
0
10
9
) to show in the default output format. We can change this
by typing:
×
>> format long e
>> C
C=
2.006702229622023e+09
-2.201930087288049e+06
6.039665477603122e+02
The backslash operator does its best to solve a system of linear equations
using Gaussian elimination or least-squares algorithms, depending on
whether the system is exact, or over- or under-determined. We can
