Partial pivoting row swapping

Question

Rabia Sonmez 2021-9-11

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1451429-partial-pivoting-row-swapping

评论： Rabia Sonmez 2021-9-13

a=[1 4 3 5;2 0 2 6;1 1 0 5;1 2 3 4];
b=[5;6;7;10]
ab=[a b]
for i=1,3
if ab(i,i)< abs(max(ab(:,i)))
     piv=ab(i,:)
      ab(i,:)=ab(i+1,:)
    ab(i+1,:)=piv
    for j=2:4
  ab(j,:)=ab(j,:)-ab(j,1)/ab(1,1)*ab(1,:)
end
end
end

Guys when I run the code I get

ab =

2 0 2 6 6

0 4 2 2 2

0 1 -1 2 4

0 2 2 1 7

I should make zero below the diagonal matrix. I did firs column but the others I could not. Can you help me? Thank you in advance.

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Answer 1

Chunru 2021-9-12

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1451429-partial-pivoting-row-swapping#answer_785599

在 MATLAB Online 中打开

a=[1 4 3 5;2 0 2 6;1 1 0 5;1 2 3 4];
b=[5;6;7;10]
b = 4×1
     5
     6
     7
    10
ab=[a b]
ab = 4×5
     1     4     3     5     5
     2     0     2     6     6
     1     1     0     5     7
     1     2     3     4    10
for i=1:size(ab, 1)-1
    % pivoting
    [~, imax] = max(abs(ab(i:end, i)));
    %ab(i:end, i)
    %imax
    
    % exchange rows
    piv=ab(imax+(i-1),:);
    ab(imax+(i-1), :)=ab(i, :);
    ab(i,    :)=piv;
    ab
    
    % elimination
    for j=i+1:size(ab, 1)
        ab(j,:)=ab(j,:)-ab(j,i)/ab(i,i)*ab(i,:)
    end
end
ab = 4×5
     2     0     2     6     6
     1     4     3     5     5
     1     1     0     5     7
     1     2     3     4    10
ab = 4×5
     2     0     2     6     6
     0     4     2     2     2
     1     1     0     5     7
     1     2     3     4    10
ab = 4×5
     2     0     2     6     6
     0     4     2     2     2
     0     1    -1     2     4
     1     2     3     4    10
ab = 4×5
     2     0     2     6     6
     0     4     2     2     2
     0     1    -1     2     4
     0     2     2     1     7
ab = 4×5
     2     0     2     6     6
     0     4     2     2     2
     0     1    -1     2     4
     0     2     2     1     7
ab = 4×5
    2.0000         0    2.0000    6.0000    6.0000
         0    4.0000    2.0000    2.0000    2.0000
         0         0   -1.5000    1.5000    3.5000
         0    2.0000    2.0000    1.0000    7.0000
ab = 4×5
    2.0000         0    2.0000    6.0000    6.0000
         0    4.0000    2.0000    2.0000    2.0000
         0         0   -1.5000    1.5000    3.5000
         0         0    1.0000         0    6.0000
ab = 4×5
    2.0000         0    2.0000    6.0000    6.0000
         0    4.0000    2.0000    2.0000    2.0000
         0         0   -1.5000    1.5000    3.5000
         0         0    1.0000         0    6.0000
ab = 4×5
    2.0000         0    2.0000    6.0000    6.0000
         0    4.0000    2.0000    2.0000    2.0000
         0         0   -1.5000    1.5000    3.5000
         0         0         0    1.0000    8.3333