On tensor tubal-Krylov subspace methods
Alaa El Ichi, Khalide Jbilou, R. Sadaka
Abstract
In this paper, we will introduce some new tubal-Krylov subspace methods for solving linear tensor equations. Using the well known tensor T-product, we will in particular define the tensor tubal-global GMRES that could be seen as a generalization of the global GMRES. We also give a new tubal-version of the tensor Golub–Kahan algorithm. To this end, we first introduce some new tensor-tensor products and new related algebraic properties. The presented numerical tests compare the two methods and show the efficiency of the proposed procedures.
Topics & Concepts
Generalized minimal residual methodKrylov subspaceMathematicsTensor productTensor product of Hilbert spacesTensor (intrinsic definition)Applied mathematicsGeneralizationTensor product of modulesTensor contractionAlgebra over a fieldMathematical optimizationMathematical analysisPure mathematicsIterative methodTensor decomposition and applicationsMatrix Theory and AlgorithmsPower System Optimization and Stability