A Modified Conjugate Residual Method and Nearest Kronecker Product Preconditioner for the Generalized Coupled Sylvester Tensor Equations
Tao Li, Qing‐Wen Wang, Xin‐Fang Zhang
Abstract
This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive a preconditioned modified conjugate residual method based on the Kronecker product approximations for solving the tensor equations. A theoretical analysis shows that the proposed method converges to an exact solution for any initial tensor at most finite steps in the absence round-off errors. Compared with a modified conjugate gradient method, the obtained numerical results illustrate that our methods perform much better in terms of the number of iteration steps and computing time.
Topics & Concepts
Kronecker productPreconditionerConjugate gradient methodMathematicsTensor productResidualConjugate residual methodKronecker deltaTensor (intrinsic definition)Applied mathematicsRate of convergenceMathematical analysisIterative methodMathematical optimizationComputer scienceAlgorithmGeometryPure mathematicsGradient descentPhysicsQuantum mechanicsComputer networkMachine learningArtificial neural networkChannel (broadcasting)Tensor decomposition and applicationsMatrix Theory and AlgorithmsAdvanced Numerical Methods in Computational Mathematics