CS 257
Numerical Methods  Homework 5
October 3, 2006
1.
[1pt]
7.3 #2
(a)
Solution:
5(
n

1) + 1 = 5
n

4. The important part is that the number of operations is
O
(
n
).
(b)
Solution:
8(
n

2) + 6 + 3(
n

2) = 11
n

16.
2.
[2pt]
7.3c #5. Turn in your implementation of
Tri()
.
function x=tri(a,d,c,b)
n = length(d);
for i=2:n
xmult = a(i1) / d(i1);
d(i) = d(i)  xmult*c(i1);
b(i) = b(i)  xmult*b(i1);
end
x(n) = b(n)/d(n)
for i=(n1):1:1
x(i) = (b(i)  c(i)*x(i+1))/ d(i);
end
Run with the following data
a = ones(99,1);
a(99) = 1;
d = 4*ones(100,1); d(1) = 4; d(100) = 4;
c = ones(99,1);
c(1) = 1;
b = 40*ones(100,1); b(1) = 20;
b(100) = 20;
x = tri(a,d,c,b)
3.
[1pt]
8.1 #1a
Solution:
L
=
1
0
0
0
1
0
1
/
3

3
1
U
=
3
0
3
0

1
3
0
0
8
4.
[1pt]
8.1 #9
Solution:
L
=
1
0
0
1
1
0
3

1
1
D
=
2
0
0
0

2
0
0
0
3
U
=
1

1
/
2
1
0
1

1
/
2
0
0
1
x
=

1
2
1
5.
[1pt]
8.1 #21
L
=
1
0
0
0
2
1
0
0

1
2
1
0
1

1
1
1
D
=
1
0
0
0
0

1
0
0
0
0
2
0
0
0
0

2
1
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6.
[1pt]
8.1 #22
L
=
2
0
0
3
4
0
5
1
6
7.
[Optional 0pt]
(a) Write a MATLAB function
[L,U]=ludoo(A)
that implements LU using the Doolittle implementation
(cf. pg. 320).
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 Fall '05
 ThomasKerkhoven
 Numerical Analysis, course webpage, Jacobi method, Iterative method, Jacobi, Doolittle

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