 A rapid and powerful iterative method for computing inverses of sparse tensors with applicationsEisa Khosravi Dehdezi and Saeed Karimi Applied Mathematics and Computation, 2022, vol. 415, issue C Abstract: This paper proposes an algorithm based on the Shultz iterative method and divided differences to find the roots of nonlinear equations. Using the new method, we present a rapid and powerful algorithm to compute an approximate inverse of an invertible tensor. Analysis of the convergence error shows that the convergence order of the method is a linear combination of the Fibonacci sequence and also is rapid and powerful in finding and keeping sparsity of the obtained approximate inverse of the sparse tensors. The algorithm is extended for computing the Moore-Penrose inverse of a tensor. As an application, we use the iterates obtained by the algorithm as a preconditioner for the tensorized Krylov subspace method, e.g., LSQR based tensor form to solve the multilinear system A★NX=B. Several examples are also provided to show the efficiency of the proposed method. Finally, some concluding remarks are given. Keywords: Tensor; Iterative method; Inverse; Moore-Penrose inverse; Einstein product (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:415:y:2022:i:c:s0096300321008043 DOI: 10.1016/j.amc.2021.126720 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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