A quasi-Newton method with modification of one column per iteration (Q798571)

We introduce a new quasi-Newton method for solving nonlinear simultaneous equations. At each iteration only one column of \(B_ k\) is changed to obtain \(B_{k+1}\). This permits to use the well-known techniques of Linear Programming for modifying the factorization of \(B_ k\). We present a local convergence theorem for a restarted version of the method. The new algorithm is compared numerically with some other methods which were introduced for solving the same kind of problems.