This paper considers different versions of block-column iterative (BCI) methods for solving nonnegative constrained linear least squares problems. We present the convergence analysis for a family of stationary BCI methods with nonnegativity constraints (BCI-NC), which is applicable to linear complementarity problems (LCP). We also consider the flagging idea for BCI methods, which allows saving computational work by skipping small updates. Also, we combine the BCI-NC algorithm and the flagging version of a nonstationary BCI method with nonnegativity constraints to derive a convergence analysis for the resulting method (BCI-NF). The performance of our algorithms is shown on ill-posed inverse problems taken from tomographic imaging. We compare the BCI-NF and BCI-NC algorithms with three recent algorithms: the inner-outer modulus method (Modulus-CG method), the modulus-based iterative method to Tikhonov regularization with nonnegativity constraint (Mod-TRN method), and nonnegative flexible CGLS (NN-FCGLS) method. Our algorithms are able to produce more stable results than the mentioned methods with competitive computational times.

本文考虑了解决非负约束线性最小二乘问题的不同版本的块列迭代（BCI）方法。我们介绍了具有非负约束（BCI-NC）的平稳BCI方法族的收敛性分析，该方法适用于线性互补问题（LCP）。我们还考虑了BCI方法的标记思想，该思想允许通过跳过小的更新来节省计算工作。此外，我们将BCI-NC算法和具有非负约束的非平稳BCI方法的标记版本相结合，以得出针对所得方法（BCI-NF）的收敛性分析。我们的算法的性能在断层成像所产生的不适定逆问题上得到了证明。我们将BCI-NF和BCI-NC算法与三种最新算法进行了比较：内外模量法（模量-CG法），带非负约束的Tikhonov正则化的基于模量的迭代法（Mod-TRN方法）和非负柔性CGLS（NN-FCGLS）法。与具有竞争力的计算时间的上述方法相比，我们的算法能够产生更稳定的结果。