  The growing availability and usage of low precision foating point formats has
attracts many interests of developing lower or mixed precision algorithms for
scientific computing problems. In this paper we investigate the possibility of
exploiting lower precision computing in LSQR for solving discrete linear
ill-posed problems. We analyze the choice of proper computing precisions in the
two main parts of LSQR, including the construction of Lanczos vectors and
updating procedure of iterative solutions. We show that, under some mild
conditions, the Lanczos vectors can be computed using single precision without
loss of any accuracy of final regularized solutions as long as the noise level
is not extremely small. We also show that the most time consuming part for
updating iterative solutions can be performed using single precision without
sacrificing any accuracy. The results indicate that the most time consuming
parts of the algorithm can be implemented using single precision, and thus the
performance of LSQR for solving discrete linear ill-posed problems can be
significantly enhanced. Numerical experiments are made for testing the single
precision variants of LSQR and confirming our results.
