Unformatted text preview: systems requires n additions for a total of
3
T he elimination step on the matrix requires 5 . Use the Gaussian Elimination w ith Partial Pivoting and Solution algorithm to solve
2 x1 2 x2 x3 4
x1 4 x2 6 x3 11
4 x1 8 x2 4 x3 4
Show w hat occupies storage in the A m atrix and the ip array initially and after each major step
of elimination. A ip 2
1
4 2
4
8 1
6
4 ?
?
? 4 8 4 3 1/4 2 5 1/2 6 3 ?
? 4
1/4 8
6 1/2 1/3 4
3
4 3
3
? 4 8 4 3 1/4 6 3 3 1/2 1/3 4 3 4
F or the elimination applied to b 11 w e 4 4 4 4
get it changing to 11 , 10 , 6 , and 4 6 10 4
finally 6 . In the bottom loop w e b3 8 8 8
and x3 2. T hen w e get
4
0
b2 6 3 2 0 so x2 0 . Finally
6
w e get b1 4 (8) 0 4 2 4 so
4
x1 1.
4 6 . Fill in the five blanks in the code for Gaussian Elimination w ith Partial Pivoting and
Solution separated from elimination:
for k = 1:n
choose ipk such that  Aipk ,k  max{ Ai ,k : i k}
if Aipk ,k 0
warning ('Pivot in Gaussian Elimination is zero')
end
swap Ak ,k ,..., Ak ,n with Aipk ,k ,..., Aipk ,n
for i = k+1:n
Ai ,k = Ai ,k / Ak ,k
for j = k+1:n
Ai , j Ai , j Ai ,k Ak , j
end
end
end
for k = 1:n
swap bk with bipk
for i = k+1:n
bi bi Ai ,k bk
end
end
for i = n:1:1
for j = i+1:n
bi bi Ai , j x j
end
xi bi / Ai ,i
end...
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This test prep was uploaded on 03/21/2014 for the course M 340L taught by Professor Pavlovic during the Spring '08 term at University of Texas.
 Spring '08
 PAVLOVIC
 Matrices

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