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nonsingular matrix (X) in GSVD function

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Francisco Carlos Parra-Rojas
Answered: Christine Tobler on 6 Apr 2020
In the description of GSVD function you consider that A = U*C*X', but in the original paper of Van Loan 1976 is A=U*C*X^-1, what is the correct form?


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Answers (1)

Christine Tobler
Christine Tobler on 6 Apr 2020
These are just different but equivalent definitions: Both will result in the same C and S, the only difference is in how X is represented.
The advantage of using X and not its inverse is that this algorithm will also work for cases where X becomes singular, where an inverse could not be taken. This happens if [A; B] does not have full rank.


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