TY - GEN A1 - Schlenkrich, Sebastian A1 - Griewank, Andreas A1 - Walther, Andrea T1 - Local Convergence of Tr1 Updates for Solving Nonlinear Equations N2 - For the solution of nonlinear equation systems quasi-Newton methods based on low-rank updates are of particular interest. We analyze a class of TR1 update formulas to approximate the system Jacobian. The local q-superlinear convergence for nonlinear problems is proved for a particular subclass of updates. Moreover, we give an estimate of the r-order of convergence. Numerical results comparing the TR1 method to Newton's and other quasi-Newton methods atr presented. KW - quai-Newton KW - TR1 Update KW - local convergence Y1 - 2006 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/337 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-3372 ER -