Extended conjugate gradient squared and conjugate residual squared methods for solving the generalized coupled Sylvester tensor equations
Eisa Khosravi Dehdezi, Saeed Karimi
Abstract
In this paper, two attractive iterative methods – conjugate gradient squared (CGS) and conjugate residual squared (CRS) – are extended to solve the generalized coupled Sylvester tensor equations [Formula: see text]. The proposed methods use tensor computations with no maricizations involved. Also, some properties of the new methods are presented. Finally, several numerical examples are given to compare the efficiency and performance of the proposed methods with some existing algorithms.
Topics & Concepts
Conjugate gradient methodConjugate residual methodMathematicsResidualTensor (intrinsic definition)Applied mathematicsDerivation of the conjugate gradient methodNonlinear conjugate gradient methodMean squared errorConjugateComputationSquare (algebra)Mathematical optimizationGradient descentAlgorithmComputer scienceMathematical analysisArtificial intelligenceArtificial neural networkGeometryStatisticsTensor decomposition and applicationsMatrix Theory and AlgorithmsAdvanced Optimization Algorithms Research