How do I compute the pseudo-inverse of a matrix using QR decomposition with column pivoting?

How do I compute the pseudo-inverse of a matrix using QR decomposition with column pivoting in MATLAB R2021b?

Answer 1

[MathWorks Support Team]

We have a function:

>> x = lsqminnorm(A, b)

which uses QR decomposition with column pivoting behind the scenes and returns the equivalent of

>> x = pinv(A)*b

If you want to do this repeatedly for different vectors “b”, you can do the following:

>> dA = decomposition(A, 'cod');
>> x = dA \ b;

While we don’t have a function that computes the pseudo-inverse itself with this method, it’s possible to get it like so:

>> lsqminnorm(A, eye(size(A, 1)))

Finally, note that in the low-rank case, “lsqminnorm” computes an additional RQ decomposition of the matrix R to get a low-rank decomposition of the matrix A (using the LAPACK function “dtzrzf”).