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With the growth of data, it is more important than ever to develop anefficient and robust method for solving the consistent matrix equation AXB=C.The randomized Kaczmarz (RK) method has received a lot of attention because ofits computational efficiency and low memory footprint. A recently proposedapproach is the matrix equation relaxed greedy RK (ME-RGRK) method, whichgreedily uses the loss of the index pair as a threshold to detect and avoidprojecting the working rows onto that are too far from the current iterate. Inthis work, we utilize the Polyak's and Nesterov's momentums to further speed upthe convergence rate of the ME-RGRK method. The resulting methods are shown toconverge linearly to a least-squares solution with minimum Frobenius norm.Finally, some numerical experiments are provided to illustrate the feasibilityand effectiveness of our proposed methods. In addition, a real-worldapplication, i.e., tensor product surface fitting in computer-aided geometrydesign, has also been presented for explanatory purpose.

On the relaxed greedy randomized Kaczmarz methods with momentum acceleration for solving matrix equation AXB=C