Verified Eigenpairs For Tensor Based On Trust-Region Method

In the field of high-risk applications,the accuracy of calculation results is very important.However,due to the accumulation of calculation errors and the finite calcu-lation precision of real numbers,the accuracy of calculation results is often affected.In the calculation of many practical problems,even small errors are likely to cause major accidents.At the same time,tensor eigenpairs are so widely used in the field of dif-fusion magnetic resonance imaging,blind source separation and so on.Therefore it is very meaningful to study the verified eigenpairs for tensor.Base on the trust-region method and interval algorithm,we study the problem of verifying Z-eigenpairs and M-eigenpairs for tensor.Firstly,the trust-region method and the inversion-free interval newton method are used to give a verification algorithm for a symmetric tensor Z-eigenpairs.The algorithm obtains the approximate solutions of Z-eigenpairs and their corresponding bounds of error,so that there must be an accu-rate Z-eigenpairs in the range of error of the approximate solutions.We use INTLAB software package in MATLAB to implement the above algorithm,and test the numer-ical examples of which the results show that the algorithm is effective.Secondly,we establish the relationship between M-eigenpairs and Z-eigenpairs by symmetric em-bedding technique.The trusted verification algorithm for partially symmetric tensor M-eigenpairs and corresponding numerical example is given.