Graphics Programs Reference
In-Depth Information
d = 6*ones(n,1); d(n) = 7;
e = -4*ones(n-1,1);
f = ones(n-2,1);
b=zeros(n,1);b(1)=3;b(n)=4;
[d,e,f] = LUdec5(d,e,f);
x = LUsol5(d,e,f,b)
The outputfrom the program is
>>x=
2.3872
4.1955
5.4586
6.2105
6.4850
6.3158
5.7368
4.7820
3.4850
1.8797
2.5
Pivoting
Introduction
Sometimes the orderinwhich the equations are presented to the solutionalgorithm
has a significant effect on the results.For example, consider the equations
2
x
1
−
x
2
=
1
−
x
1
+
2
x
2
−
x
3
=
0
−
x
2
+
x
3
=
0
The corresponding augmented coefficient matrix is
⎡
⎣
⎤
⎦
−
2
1
0
1
A
b
=
−
12
−
1
0
(a)
0
−
110
Equations(a) are in the “right order” in the sense that we would have notrouble
obtaining the correct solution
x
1
=
x
2
=
x
3
=
1byGauss elimination orLU decom-
position. Now suppose that weexchange the first and third equations, so that the
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