Abstract
In this paper, we mainly develop the well-known vector and matrix polynomial extrapolation methods in tensor framework. To this end, some new products between tensors are defined and the concept of positive definitiveness is extended for tensors corresponding to T-product. Furthermore, we discuss on the solution of least-squares problem associated with a tensor equation using Tensor Singular Value Decomposition (TSVD). Motivated by the effectiveness of some proposed vector extrapolation methods in earlier papers, we describe how an extrapolation technique can be also implemented on the sequence of tensors produced by truncated TSVD (TTSVD) for solving possibly ill-posed tensor equations.
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The authors would like to express their sincere thanks to the anonymous referee for his/her useful comments which improved the quality of paper.
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Beik, F.P.A., Ichi, A.E., Jbilou, K. et al. Tensor extrapolation methods with applications. Numer Algor 87, 1421–1444 (2021). https://doi.org/10.1007/s11075-020-01013-5
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DOI: https://doi.org/10.1007/s11075-020-01013-5