What algorithm does mldivide use for rectangular matrices

I have a sparse matrix A involved in Ax=b for A the vertical size is larger than horizontal size does mldivide use sparse QR factorization or another method and in case I make a delta change in A(dA), and delta changes in b (db) then the delta change in x (dx) would be dx=mdldivide((A+dA),(db-dA.x)) newx=x+dx does it use show improvement in time than to use newx=mldivide((A+dA),(b+db))