[Math] Can we make such matlab code so that every time we run the program it will return the same randomly generated matrices

MATLAB

I want to compare efficiency of two iteration methods for computing inverse of a matrices. I want to test performance of these methods on some randomly generated matrices. I want to know can we make such matlab code so that every time we run the program it will return the same randomly generated matrices. Could anybody answer me? I would be very much greatfull to you.

Thanks

Best Answer

In the new versions, use rng('default') to set the seed for the random number generator.

In older versions, it is something like rand('seed','twister'); but I don't remember exactly.

Either way, the first method is recommended by MATLAB.

Edit: here is code to generate random matrix of size $100$

n=100; %size of matrix
rng('default'); % set random seed to matlab default
A = rand(n,n); % generate random matrix

If you run this same code multiple times, you will get the same A each time.

Related Solutions

[Math] How to determine stopping criteria in iterative methods

For iterative methods the difference from one iteration to the other gets lower and lower as it is supposed to converge. Therefore absolute error or absolute squared error from one iteration to the other is usually defined as the stopping criterion. Of course there is one other way, that is to fix the number of iterations which is trivial. Important of choosing a threshold for the absolute error from one iteration to the next provides you a certain level of quality. If you set it to $10^{-8}$ it will take more time for the convergence but the quality of the approximation will be of course better than the case where you set it to $10^{-4}$. It is all related to the trade-off between speed of convergence and the quality of convergence which is determined by the user.

In your example, the thresholds are determined in a similar way. It is a subjective process but the quality can be objectively evaluated.

[Math] Need matlab help related with the iteration method

The prep before your loop should stay the same. The appropriate script is

A = ...; % as you have given
beta = ...; % whatever you want
X0 = beta*A'; % calculate initial estimate

% (these initial values may need to be changed, I don't have a copy of
%    matlab in front of me)    
dklast = NaN; dk = NaN; % initialise to begin loop

iter = 0;
maxiter = 100;

while (abs(dk/dklast - beta - 1) > 1e-4) && (iter < maxiter) % loop until tolerance met
    iter = iter + 1; % keep count of iteration

    X1 = (1+beta)*X0 -beta*X0*A*X0; % calculate new iterate

    dklast = dk; % move old difference "new estimate to previous iterate"
    dk = norm(X1-X0,'fro'); % determine new difference 

    X0 = X1; % copy current iterate to "old" iterate for next iteration

end

I am wondering why you are using this convergence test at all. I would recommend using

dk = norm(X1*X0-I,'fro');

which measures how close X1 is to the left inverse of $A$. Your termination criteria would then be

while dk > (some_tolerance) && iter < maxiter
    ....
end

As you currently have, you are measuring how much X1 changes from X0, which may be small, but still not an approximate inverse (or pseudoinverse) for $A$.

Best Answer

Related Solutions

[Math] How to determine stopping criteria in iterative methods

[Math] Need matlab help related with the iteration method

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