Trustworthy Verification Of Symmetric Tenser Eigenpairs Based On Adaptive Trust Region Method

In the field of high-risk applications,the accuracy of calculation results is crucial.However,the accuracy of calculation results is often affected by the accumulation of calculation errors and the finite calculation precision of real numbers.And in the ap-plication of solving practical problems,small errors in the calculation process are also likely to have a huge impact and lead to serious accidents.At the same time,tensor eigenpairs have important applications in biology?physics and other fields.There-fore,it is of great significance to study the credibility verification problem of tensor eigenpairs.In this thesis,base on the adaptive trust region method and interval algorithm theory,we study the credible verification of symmetric tensor H-eigenpairs and sym-metric tensor generalized eigenpairs.Firstly,the symmetric tensor H-eigenpairs are transformed into a homogeneous polynomial optimization problem,combined with the adaptive trust region algorithm and the non-inverse interval Newton iteration method,and the credible verification algorithm for the symmetric tensor H-eigenpairs is given.The algorithm not only obtains the approximate solution and its corresponding error bounds,but also makes that there must be an exact solution within the error bounds.Secondly,the symmetric tensor generalized eigenpairs are combined with the nonlinear programming problem,and a credible verification problem of symmetric tensor gener-alized eigenpairs is proposed.Finally,the algorithm is implemented using the INTLAB software package in Matlab,and a numerical example proves the effectiveness of the algorithm.