Recursive "pinv" function?

Has a recursive version of the "Moore-Penrose Pseudoinverse" function ("pinv") ever been done in Matlab?

Say for instance, I've got two inputs x1 and x2, where

x1 = [1 1]
x2 = [1 2]

If I do the pinv of x1, pinv(x1), I get an output of:

    0.5000
    0.5000

Including the other input, x2, like if I did,

T = [x1; x2] , and then did, pinv(T), I get an output of

    2.0000   -1.0000
   -1.0000    1.0000

Using just the result of pinv(x1) and the second input, x2,

would it be possible to get the same result as as pinv(T)?

It seems the theory for a recursive Moore-Penrose Pseudoinverse exists (here) and it would be helpful to know if there had been any Matlab code implementation publicly available.