Quasi-Newton Updates in Abstract Vector Spaces
Mike Todd · SIAM Review · 1984
We derive least-change updates of linear mappings that approximate derivatives of functions defined on abstract vector spaces; these correspond to well-known matrix updates. Our approach has the value of demonstrating the minimal assumptions necessary to derive particular updates, and hence their robustness. In addition, the choice of one or other update is indicated by the presence of natural inner or scalar products in the vector spaces. All spaces considered are finite-dimensional real vector spaces.