  Based on the joint bidiagonalization process of a large matrix pair
$\{A,L\}$, we propose and develop an iterative regularization algorithm for the
large scale linear discrete ill-posed problems in general-form regularization:
$\min\|Lx\| \ \mbox{{\rm subject to}} \ x\in\mathcal{S} = \{x|\ \|Ax-b\|\leq
\tau\|e\|\}$ with a Gaussian white noise $e$ and $\tau>1$ slightly, where $L$
is a regularization matrix. Our algorithm is different from the hybrid one
proposed by Kilmer {\em et al.}, which is based on the same process but solves
the general-form Tikhonov regularization problem:
$\min_x\left\{\|Ax-b\|^2+\lambda^2\|Lx\|^2\right\}$. We prove that the iterates
take the form of attractive filtered generalized singular value decomposition
(GSVD) expansions, where the filters are given explicitly. This result and the
analysis on it show that the method must have the desired semi-convergence
property and get insight into the regularizing effects of the method. We use
the L-curve criterion or the discrepancy principle to determine $k^*$. The
algorithm is simple and effective, and numerical experiments illustrate that it
often computes more accurate regularized solutions than the hybrid one.
