Accelerated Algorithms for Silrtc and Halrtcalgorithms by Fast Tri-Factorization Method

Tensor completion is one of the efficient methods for restoring datasuch that minimizing the rank of the tensor leads to an appropriate solution.However, it gives a non-convex objective function, which generates an NP-hardproblem. To overcome this problem, instead of using the rank function, thetrace norm is applied. To solve this problem, two heuristic algorithms, SimpleLow Rank Tensor Completion (SiLRTC) and High Accuracy Low Rank TensorCompletion (HaLRTC) can be used. In the methods based on trace norm, theSingular Value Decomposition (SVD) is used, which increases computationalcomplexity of these methods with increasing dimensions. In order to reducethe computational complexity of SVD, the method of Fast Tri-Factorization(FTF) can be utilized. In this paper, to accelerate the convergence speed ofSiLRTC and HaLRTC Algorithms, two new combined methods FTF-SiLRTCand FTF-HaLRTC are presented. Additionally, the computational complexityof all algorithms is verified. 2010 Mathematics Subject Classification. Primary 15A18; Secondary 15A69, 74B99.