This solution was first proposed in 1986 by Ciccotti and Ryckaert under the title "the matrix method", yet differed in the solution of the linear system of equations. Ciccotti and Ryckaert suggest inverting the matrix J σ σ directly, yet doing so only once, in the first iteration. The first iteration then costs O ( n 3 ) operations, whereas the following iterations cost only O ( n 2 ) operations (for the matrix-vector multiplication). This improvement comes at a cost though, since the Jacobian is no longer updated, convergence is only linear, albeit at a much faster rate than for the SHAKE algorithm.