Positive definite solution

Question

dab483 2011-11-23

1
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https://ww2.mathworks.cn/matlabcentral/answers/22034-positive-definite-solution

i need to solved for different values of gama until its lowest value, which gives a positive definite solution for P is found, so i am using all(eig(P)>0) like the equation below:

is this right?

gama=100000;
for i=1:2000;
        P = inv(inv(P)+M'*inv(R)*M-gama^(-2)*eye(4));
        E=eig(P_cov);
        if all(eig(P))>0)  %%(all eigenvalues must be positive)
          gama=gama/2;
        else
            break;      
        end
   end
P = inv(inv(P)+M'*inv(R)*M-gama^(-2)*eye(4));

is this correct?

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Answer 1

Walter Roberson 2011-11-23

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If the eigenvalues are all positive, you change gama, exiting the loop when they are not all positive. That means that at the end the gama you get out will be such that the eigenvalues are not all positive. This does not satisfy the stated conditions.

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Walter Roberson 2011-11-23

gama=100000;

oldgama = gama;

...

if all(eig(P))>0) %%(all eigenvalues must be positive)

oldgama = gama;

gama=gama/2;

else

break;

end

Then right after the end of the "for" loop,

gama = oldgama;

dab483 2011-11-24

Thank you. It satisfy the stated conditions.

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Answer 2

Sean de Wolski 2011-11-23

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https://ww2.mathworks.cn/matlabcentral/answers/22034-positive-definite-solution#answer_29055

Use a second variable and only update it if the eigenvalues are all positive. When you exit the loop it will be the last set of all positive eigenvalues.