Graphics Programs Reference
In-Depth Information
b(n) = b(n)/d(n); % Back substitution
b(n-1) = b(n-1)/d(n-1) - e(n-1)*b(n);
fork=n-2:-1:1
b(k) = b(k)/d(k) - e(k)*b(k+1) - f(k)*b(k+2);
end
x=b;
EXAMPLE 2.9
As aresult of Gauss elimination, a symmetric matrix
A
wastransformed to the upper
triangular form
⎡
⎣
⎤
⎦
−
4
2
1
0
0
3
−
3
/
2
1
U
=
00 3
−
3
/
2
00
035
/
12
Determine the original matrix
A
.
Solution
First we find
L
in the decomposition
A
=
LU
. Dividing each row of
U
by its
diagonal element yields
⎡
⎣
⎤
⎦
1
−
1
/
21
/
4
0
0
1
−
1
/
21
/
3
L
T
=
0
0
1
−
1
/
2
0
0
0
1
Therefore,
A
=
LU
becomes
⎡
⎣
⎤
⎦
⎡
⎣
⎤
⎦
1
0
0
0
4
−
2
1
0
−
1
/
2
1
00
0
3
−
3
/
2
1
A
=
/
−
/
−
/
1
4
1
2
1 0
00 3
3
2
0
1
/
3
−
1
/
21
00
035
/
12
⎡
⎣
⎤
⎦
4
−
210
−
2
4
−
21
=
1
−
2
4
−
2
0
1
−
2
4
EXAMPLE 2.10
Determine
L
and
D
that result fromDoolittle's decomposition
A
LDL
T
of the sym-
=
metric matrix
⎡
⎣
⎤
⎦
3
−
33
A
=
−
351
31 0
Search WWH ::
Custom Search