Structured linear/nonlinear multiparameter eigenvalue problems arise in many applications, such as the multiparameter Sturm-Liouville theory, the analysis of the asymptotic stability of the delay differential equation, the reconstruction of the physical mass-spring system and the semi-structured aeroelastic flutter problems.

  In this talk, I will introduce the background of the multiparameter eigenvalue problems, and then introduce two classes of numerical methods: those that deal with the problems directly and those that compute the eigenvalues of the transformed simultaneous eigenvalue problems. Finally, some theoretical analysis and numerical experiments are presented to illustrate the advantages and disadvantages of these two classes of methods.