Randomized coordinate descent method for inconsistent tensor linear systems with t-product.

Abstract A randomized coordinate descent method is proposed for solving inconsistent tensor linear systems with t-product. Theoretical analysis proves that the new method converges to the least-squares solution of the system in expectation at a linear convergence rate, which is faster than the tensor randomized extended Kaczmarz method. Its Fourier version is also analyzed, and the convergence property is provided. Numerical experiments verify the efficiency of the tensor randomized coordinate descent methods, which outperform the existing iterative methods in solving inconsistent tensor linear systems. Mathematics Subject Classification 65F10 · 65F20