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<p>We study a greedy coordinate descent method to solve large linear least-squares problems expanding on a randomized coordinate descent method presented by Leventhal and Lewis (Math. Oper. Res. 35: 641–654, 2010). For an overdetermined system, they proved its exponential convergence, regardless of its consistency. In our work, we study a greedy selection rule for the coordinate descent method which we refer to as the two-dimensional maximal residual Gauss-Seidel (D2MRGS) method. In this method, we select two coordinates in every iteration and treat the current approximation in those directions. Convergence is analyzed for the stated method and numerical experiments are provided to demonstrate its efficiency.</p>

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A Maximal Residual Two Subspace Projection Algorithm for Solving Least-Squares Problems

  • 期刊论文

  • 发表日期：

    2025年5月31日

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  • Ashif Mustafa,
  • Manideepa Saha

摘要

We study a greedy coordinate descent method to solve large linear least-squares problems expanding on a randomized coordinate descent method presented by Leventhal and Lewis (Math. Oper. Res. 35: 641–654, 2010). For an overdetermined system, they proved its exponential convergence, regardless of its consistency. In our work, we study a greedy selection rule for the coordinate descent method which we refer to as the two-dimensional maximal residual Gauss-Seidel (D2MRGS) method. In this method, we select two coordinates in every iteration and treat the current approximation in those directions. Convergence is analyzed for the stated method and numerical experiments are provided to demonstrate its efficiency.