Adaptive methods for high-dimensional eigenvalue problems and their computational complexity (C09#)

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The subject of this project are numerical solvers for high-dimensional eigenvalue problems that combine adaptive discretisations with low-rank representations of coefficient sequences. A main objective is to establish optimality properties concerning discretisation cardinalities, arising tensor ranks, and total computational complexity. This requires in particular new techniques for a posteriori error estimation and for preconditioning with low-rank tensor decompositions. As a particular application, Schrödinger equations in occupation number representation are considered.