Convergence of Quasi-Newton Method by Modified SR1 Update
Li Huanqin,Xu Chengxian
(Xi'an Jiaotong University, Xi'an 710049, China)

Abstract: In order to shown some superiority of the modified quasi-Newton methods based on the new quasiª²Newton equations over the usual quasi-Newton methods from the theoretical point of view, A symmetric rank-one method that satisfies the new quasi-Newton equation is investigated. It is proved that this algorithm generates at least p q -superlinear steps out of every n+p steps, and hence the convergence rate is 2n-step q-quadratic under the condition that the sequence of variable metric matricesis positive definite and uniformly bounded.
Keywords: new quasi-Newton method; SR£± update; convergence