This paper is concerned with a new approach for preconditioning
large sparse least squares problems. Based on the idea of the
approximate inverse preconditioner, which was originally developed
for square matrices, we construct a generalized approximate
inverse (GAINV) $M$ which approximately minimizes $\|I-MA\|_{\mathrm{F}}$ or
$\|I-AM\|_{\mathrm{F}}$. Then, we also discuss the theoretical issues such as
the equivalence between the original least squares problem and the
preconditioned problem. Finally, numerical experiments on problems
from Matrix Market collection and random matrices show that although
the preconditioning is expensive, it pays off in certain cases.