GRADIENT-BASED ITERATIVE ALGORITHMS FOR THE TENSOR NEARNESS PROBLEMS ASSOCIATED WITH SYLVESTER TENSOR EQUATIONS

This paper is concerned with the solution of the tensor nearness problem associated with the Sylvester tensor equation represented by the Einstein product. We first proposed a gradient-based iterative algorithm for the Sylvester tensor equation mentioned above, and then the solution to the tensor nearness problem under consideration can be obtained by finding the least F-norm solution of another Sylvester tensor equation with special initial iteration tensors. It is shown that the solution to the above tensor nearness problem can be derived within finite iteration steps for any initial iteration tensors in the absence of roundoff errors. The performed numerical experiments show that the algorithm we propose here is efficient.