Iterative solutions of generalized Sylvester quaternion tensor equations
Xin‐Fang Zhang, Tao Li, Yigui Ou
Abstract
This paper is concerned with the iterative solutions to a class of generalized Sylvester quaternion tensor equations. From the Kronecker product and the properties of quaternion tensors, we propose the biconjugate A-orthogonal residual stabilized and the generalized product-type biconjugate A-orthogonal residual methods in their tensor forms for solving the original tensor equation. As an application, the proposed methods are tested with some colour video restoration problems. Numerical results show the effectiveness of our methods compared with some existing methods.
Topics & Concepts
QuaternionMathematicsTensor (intrinsic definition)ResidualKronecker productCartesian tensorTensor productAlgebra over a fieldApplied mathematicsTensor fieldMathematical analysisTensor densityPure mathematicsKronecker deltaAlgorithmExact solutions in general relativityGeometryPhysicsQuantum mechanicsTensor decomposition and applicationsElasticity and Material ModelingMatrix Theory and Algorithms