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Numerical subspace algorithms for solving the tensor equations involving Einstein product
Author(s) -
Huang Baohua,
Li Wen
Publication year - 2021
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.2351
Subject(s) - conjugate residual method , biconjugate gradient method , mathematics , conjugate gradient method , tensor (intrinsic definition) , biconjugate gradient stabilized method , tensor product of hilbert spaces , nonlinear conjugate gradient method , residual , subspace topology , cartesian tensor , krylov subspace , derivation of the conjugate gradient method , tensor contraction , mathematical analysis , tensor product , symmetric tensor , tensor density , algorithm , tensor field , exact solutions in general relativity , iterative method , geometry , gradient descent , pure mathematics , computer science , artificial intelligence , artificial neural network
In this article, we propose some subspace methods such as the conjugate residual, generalized conjugate residual, biconjugate gradient, conjugate gradient squared and biconjugate gradient stabilized methods based on the tensor forms for solving the tensor equation involving the Einstein product. These proposed algorithms keep the tensor structure. The convergence analysis shows that the proposed methods converge to the solution of the tensor equation for any initial value. Some numerical results confirm the feasibility and applicability of the proposed algorithms in practice.