Create for loop in a matrix (power method)

Question

Roy dela Rama 2016-3-9

0
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https://ww2.mathworks.cn/matlabcentral/answers/272264-create-for-loop-in-a-matrix-power-method

回答： Roy dela Rama 2016-3-9

Estimate the most dominant eigenvalue of [A] and its corresponding eigenvector,using the power method.

 A = [4  3  1;
      3 -6  0;
      1  0  2];
 B = [1;     
      1;
      1];
 n = 50;         % number of iterations
    C = A*B      % iterative equation
    [maxC, index] = max (abs(C(:)));
    maxC = maxC * sign(C(index)) 
                 % largest magnitude in matrix C (courtesy of IMAGE ANALYST)
    D = C/maxC   % factor out the largest magnitude in matrix C
    B = D        % this is the new value of B

I want to use the new value of B in C = A*B until it reaches 50 iterations. Expected answers are

 maxC = -6.83909 
 D = -0.279693
      1
      0.0316436

I get an error message whenever I try the for loop..

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Answer 1

Roy dela Rama 2016-3-9

0
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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/272264-create-for-loop-in-a-matrix-power-method#answer_212907

在 MATLAB Online 中打开

I already figured it out. I don't need to use C(i+1) for my iteration equation for this particular matrix.

All I have to do is proceed with for loop:

 for i = 1:n;
        C = A*B      
        [maxC, index] = max (abs(C(:)));
        maxC = maxC * sign(C(index)) 
        D = C/maxC   % factor out the largest magnitude in matrix C
        B = D        % this is the new value of B
end