Numerically approximate all the singular values of a positive definite matrix:
Compare with the numerical values of the exact singular values:
Some values less than the default tolerance are computed poorly due to numerical roundoff:
Get the complete singular value decomposition of a nearly singular matrix:
Reconstruct the matrix:
Without the setting for
Tolerance, the matrix is considered effectively singular:
Detect maximum possible numerical rank:
The two rows are only detected as independent because of representation error:
The default tolerance allows for the numerical representation error:
Limit roundoff error at the expense of a larger residual for a least squares problem:
With the default tolerance, numerical roundoff is limited so error is distributed:
Specifying a higher tolerance will limit roundoff errors at the expense of a larger residual:
With
Tolerance
, numerical roundoff can introduce excessive error:
of the largest singular value:
EXAMPLES
Basic Examples 
Scope 