Graphics Programs Reference
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A(i,k) = lambda;
end
end
end
Solution phase
Considernow the procedurefor solving
Ly
=
b
by forward substi-
tution. The scalar form of the equations is(recall that
L
ii
=
1)
y
1
=
b
1
L
21
y
1
+
y
2
=
b
2
.
L
k
1
y
1
+
L
k
2
y
2
+···+
L
k
,
k
−
1
y
k
−
1
+
y
k
=
b
k
.
Solving the
k
th equation for
y
k
yields
k
−
1
y
k
=
b
k
−
=
,
,...,
L
kj
y
j
,
k
2
3
n
(2.14)
j
=
1
Letting
y
overwrite
b
, weobtain the forward substitutionalgorithm:
fork=2:n
y(k)= b(k) - A(k,1:k-1)*y(1:k-1);
end
The back substitutionphase for solving
Ux
=
y
is identicaltothat usedinthe
Gauss eliminationmethod.
LUsol
Thisfunction carries out the solutionphase (forward and back substitutions). It is
assumed that the original coefficient matrix has beendecomposed,sothat the input
is
A
=
\
.
The contents of
b
are replacedby
y
during forward substitution. Similarly,
back substitution overwrites
y
with the solution
x
[
L
U
]
.
functionx=LUsol(A,b)
% Solves L*U*b = x, where A contains both L and U;
%thatis,Ahastheform[L\U].
%USAGE:x=LUsol(A,b)
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