Singular Matrices: Is the Matlab algorithm for CONDITON NUMBER always stable ?

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Richard Coates
Richard Coates on 7 Nov 2019
Commented: John D'Errico on 7 Nov 2019
Their documentation says that their algorithm for determinants can be unstable because of problems with LU factorization.
Their documenatio for cindition number - COND - does not mention stability problems, even though some algorithms use LU factorization I believe.

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Answers (1)

Richard Brown
Richard Brown on 7 Nov 2019
The algorithm for condition number uses the SVD, not LU factorisation and is perfectly stable.
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John D'Errico
John D'Errico on 7 Nov 2019
Yes. As well, there are very few cases where you really want to use det for anything anyway. You certainly never want to use it to determine the singularity of a matrix, despite what they always teach students in class.

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