Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian

For solving large systems of nonlinear equations by quasi-Newton methods it may often be preferable to store an approximation to the Jacobian rather than an approximation to the inverse Jacobian. The main reason is that when the Jacobian is sparse and the locations of the zeroes are known, the updating procedure can be made more efficient for the approximate Jacobian than for the approximate inverse Jacobian.