Numerical Algorithms https://doi.org/10.1007/s11075-020-00932-7 ORIGINAL PAPER Column-oriented algebraic iterative methods for nonnegative constrained least squares problems T. Nikazad 1 · M. Karimpour 1 Received: 30 July 2019 / Accepted: 5 April 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract 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 con- straints (BCI-NC), which is applicable to linear complementarity problems (LCP). We also consider the flagging idea for BCI methods, which allows saving computa- tional 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 algo- rithms: 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. Keywords Row and column-block methods · Linear complementarity problems · Flagging · Constrained linear least squares problems · Relaxation parameter Mathematics Subject Classification (2010) 65F10 · 65R32  T. Nikazad tnikazad@iust.ac.ir M. Karimpour mkarimpoursb@yahoo.com 1 School of Mathematics, Iran University of Science and Technology, 16846-13114, Tehran, Iran