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Solving coupled tensor equations via higher order LSQR methods
Author(s) -
Masoud Hajarian
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2013419h
Subject(s) - mathematics , tensor (intrinsic definition) , tensor product , order (exchange) , product (mathematics) , algebra over a field , einstein tensor , pure mathematics , riemann curvature tensor , geometry , finance , curvature , economics
Tensors have a wide application in control theory, data mining, chemistry, information sciences, documents analysis and medical engineering. The material here is motivated by the development of the efficient numerical methods for solving the coupled tensor equations (A1*M X *N B1 + C1 *M Y *N D1 = E1, A2 *M X *N B2 + C2 *M Y *N D2 = E2, with Einstein product. We propose the tensor form of the LSQR methods to find the solutions X and Y of the coupled tensor equations. Finally we give some numerical examples to illustrate that our proposed methods are able to accurately and efficiently find the solutions of tensor equations with Einstein product.

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