THE RELATIONSHIP BETWEEN THE APPROXIMATE HESSIAN MATRICES GENERATED BY A CLASS OF QUASI-NEWTON METHODS

摘要

In this report it is shown how, under certain conditions, the approximation to the Hessian matrix generated by using one quasi-Newton method is related to the approximation obtained using an alternative method. Dixon (1971) has shown that under the same conditions the directions of search generated by a certain class of quasi-Newton methods are identical apart from a scalar multiplier. Dixon's result and the value of the scalar multiplier are a direct consequence of the relationship derived in this report between the approximate Hessian matrices.