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Recently, I studied A research paper where author has compared his proposed method with several other existing method on a randomly sigular matrices with fixed condition number. My question is can we generate a random matrices with desired condition number using matlab?

Here is the link of paper: An improved method for the computation of the Moore-Penrose inverse matrix, table 3

Please clarify my doubt. I would be very much thankful to you.

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    I think the question has a little problem. Singular matrices have at least one singular value equals zero.2012-09-18

1 Answers 1

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Matrices in Table 3 are well-known matrices which are close to singular. The condition number is defined as the ratio between the maximal and the minimal singular values. In order to generate a matrix with a desired condition number, you can use SVD decomposition and modify the matrix with the singular values:

nr=4; %Number of rows nc=5; %Number of columns CondNumb=10*sqrt(2); %Desired condition number A=randn(nr,nc); [U,S,V]=svd(A); S(S~=0)=linspace(CondNumb,1,min(nr,nc)); A=U*S*V'; 

Regards, Fernando

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    You are welcome! I edit the original code for rectangular matrices. Hope it helps.2012-09-20