A New Feasible Trust-region Method For Tensor Z-eigenvalues Problems With Second-order Correction

Tensor have been more concerned in automatic control,magnetic resonance imaging,face recognition and other fields.The largest Z-eigenvalues give rise to the best rank-1 approximation of tensor and the smallest Z-eigenvalues can be applied to determine the positive definiteness of an even order symmetric tensor,which play important part in Taylor formula,diffusion tensor imaging,automatic control and independent component analysisThe feasible trust-region method is an effective method to find the z-eigenvalue of the tensor.Construct the trust-region subproblem at the current iteration point x,and get dk to solve it.The constraint of trust-region subproblem is obtained by linearizing the spherical constraintThis paper proposes a feasible trust-region method with second-order correction by adding the second-order correction term(?)d to the linear constraint of the feasible trust region method To make the algorithm stablely,we add a parameter a into the second-order correction term We can prove that the trust-region subproblem with the second-order correction term is compat-ible,which shows that the subproblem is feasible.The numerical results show that the feasible trust-region method with the second-order correction term can obtain the same eigenvalue as the trust-region method with less calculation timeThis paper is divided into three chapters.The first chapter mainly introduces the defini-tions of tensor and its eigenvalues,the algorithms for calculating eigenvalues and applications The second chapter introduces the feasible trust-region method,then gives the new feasible trust-region method with the second-order correction term.The third chapter gives the algo-rithm of the feasible trust-region method with the second-order correction term.The numerical experiments are carried out and compared with the numerical results of the feasible trust-region method.