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Krylov subspace methods to solve a class of tensor equations via the Einstein product
Author(s) -
Huang Baohua,
Xie Yajun,
Ma Changfeng
Publication year - 2019
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.2254
Subject(s) - mathematics , krylov subspace , tensor contraction , tensor product of hilbert spaces , cartesian tensor , lanczos resampling , tensor product , generalized minimal residual method , tensor (intrinsic definition) , lanczos tensor , symmetric tensor , tensor density , algebra over a field , mathematical analysis , iterative method , exact solutions in general relativity , tensor field , pure mathematics , mathematical optimization , eigenvalues and eigenvectors , physics , quantum mechanics
Summary This paper is concerned with some of the well‐known iterative methods in their tensor forms to solve a class of tensor equations via the Einstein product. More precisely, the tensor forms of the Arnoldi and Lanczos processes are derived and the tensor form of the global GMRES method is presented. Meanwhile, the tensor forms of the MINIRES and SYMMLQ methods are also established. The proposed methods use tensor computations with no matricizations involved. Numerical examples are provided to illustrate the efficiency of the proposed methods and testify the conclusions suggested in this paper.