Various methods have been suggested for computing simple bifurcation points. Some of these methods greatly enlarge the dimension of the system of equations to be solved. This paper gives a characterization of a simple bifurcation point which replaces an n dimensional system by an auxiliary system of dimension n + 2 whose Jacobian is nonsingular at the corresponding zero. This minimal extension is an attractive feature of the method.

A detailed description is given of a Newton-like algorithm for solving the nonlinear system. It involves use of difference quotient approximations for derivatives. The algorithm is shown to be R-quadratically convergent. Three simple examples are given to illustrate the performance of the method.

The paper is rather specialized. However, sufficient detail is included to fully describe the method presented.