Preconditioned tensor splitting AOR iterative methods for ℋ‐tensor equations
Xuezhong Wang, Maolin Che, Yimin Wei
Abstract
Summary Based on the weak regular splitting of tensors, preconditioned technology has shown great advantages in solving tensor equations with nonsingular (strong) ‐tensors. In this article, we introduce H ‐splitting and H ‐compatible splitting and investigate the relationship between these different splittings and their convergence. Meanwhile, we also consider a preconditioned AOR iterative method for solving tensor equations with nonsingular ‐tensors. We prove its convergence and give a comparison result on the spectral radius of the iteration tensor for the case when is a nonsingular ‐tensor. Numerical examples are also given to illustrate our methods.
Topics & Concepts
MathematicsInvertible matrixTensor (intrinsic definition)Spectral radiusConvergence (economics)Tensor calculusIterative methodMathematical analysisApplied mathematicsExact solutions in general relativityPure mathematicsTensor fieldMathematical optimizationEigenvalues and eigenvectorsPhysicsQuantum mechanicsEconomic growthEconomicsTensor decomposition and applicationsMatrix Theory and AlgorithmsAdvanced Numerical Methods in Computational Mathematics