Sparse two-sided rank-one updates for nonlinear equations

The two-sided rank-one (TR1) update method was introduced by Griewank and Walther (2002) for solving nonlinear equations. It generates dense approximations of the Jacobian and thus is not applicable to large-scale sparse problems. To overcome this difficulty, we propose sparse extensions of the TR1 update and give some convergence analysis. The numerical experiments show that some of our extensions are superior to the TR1 update method. Some convergence analysis is also presented.