Tuning-Free Distributed Least-Squares Algorithm for Linear Algebraic Equations with Sum-Separable Data

This letter investigates the distributed least-squares (LS) problem for a multi-agent system. Unlike conventional distributed frameworks where data is partitioned row-wise or column-wise, we consider a summation-based formulation where the global coefficient matrix and supply vector are the sums of local submatrices and subvectors, respectively. Each agent possesses only its local pair of data, necessitating a decentralized approach. Leveraging a recent tuning-free discretization method studied in Liu and Si (2026), we develop a novel discrete-time distributed algorithm that does not require manual step-size tuning-a common bottleneck in existing methods. Rigorous convergence analysis demonstrates that, under a mild condition on the single design parameter-independent of the problem data-the algorithm converges exponentially to a LS solution of the linear algebraic equation with sum-separable data.