A faster Broyden method (Q1176832)

The paper is concerned with the inverse-secant method of \textit{C. G. Broyden} [Math. Comput. 19, 577--593 (1965; Zbl 0131.13905)] for solving the system of nonlinear equations. The author gives two remarks on the cost of one step of two variants of the algorithm. The first comment states that one step of Broyden's mMethod One involves about \(3n^2\) multiplications and additions, whereas Method Two about \(2n^2\). In the second remark it is explained how \(n^2\) multiplications needed for finding the next value \(x\) can be avoided.