TY - GEN A1 - Griewank, Andreas A1 - Schlenkrich, Sebastian A1 - Walther, Andrea T1 - Adjoint Broyden a la GMRES N2 - It is shown here that a compact storage implementation of a quasi-Newton method based on the adjoint Broyden update reduces in the affine case exactly to the well established GMRES procedure. Generally, storage and linear algebra effort per step are small multiples of $n\cdot k$, where $n$ is the number of variables and $k$ the number of steps taken in the current cycle. In the affine case the storage is exactly $(n+k)\cdot k$ and in the nonlinear case the same bound can be achieved if adjoints, i.e. transposed Jacobian-vector products are available. A transposed-free variant that relies exclusively on Jacobian-vector products (or possibly their approximation by divided differences) requires roughly twice the storage and turns out to be somewhat slower in our numerical experiments reported at the end. Y1 - 2007 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/424 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-4243 ER -