BIT Numerical Analysis is celebrating its 65:th anniversary with a three day conference on the 14:th-16:th of January, in Uppsala, Sweden. Link.
I will be holding a presentation on ongoing work with my supervisor. We are developing a new method for a particular class of nonlinear eigenvalue problems with eigenvector nonlinearities (NEPv), motivated by the Gross-Pitaevskii eigenvalue problem. You can find my abstract below.
Abstract: We study eigenvalue problems in which there is a nonlinear dependence on the eigenvector, abbreviated NEPv. In this sense, these problems generalize the familiar linear eigenvalue problem. Specifically, we consider nonlinearities that appear as a sum of products of scalar functions of the eigenvector, and rank-one matrices. The target problems may contain many such nonlinear terms. Our attention is focused on exploiting this and similar structures that appear for instance in the Gross-Pitaevskii equation. To this end we present a method for reformulating the class of problems of this form into equivalent problems with eigenvalue nonlinearities (NEP), enabling us to use efficient methods for these problems as a means of obtaining solutions to the NEPv. In particular, these methods can efficiently compute several eigenvalues. We show how the transformation from NEPv to NEP can be constructed theoretically, and indicate how it can be handled in practice. Numerical experiments demonstrate the effectiveness of our approach.