Abstract of Antonio Falco Montesinos

On the convergence of the greedy rank-one update algorithm
We study the convergence of the well-known greedy rank-one update alkgorithm. It is used to construct the rank-one tensor series solution either for full-rank linear systems or for elliptic problems in abstract form. The existence of the rank-one approximations is also not new, but surprisingly the focus there has been more on the applications side than in the convergence ananlysis. Moreover, we discuss the relationship with the so-called proper generalized decomposition used in engineering applications.


Lars Grasedyck (MPI Leipzig, Germany)
Wolfgang Hackbusch (MPI Leipzig, Germany)
Boris Khoromskij (MPI Leipzig, Germany)