A Bisection-Like Algorithm for Branch Switching at a Simple Branch Point

At a Simple Branch Point x0 of a parameter-dependent nonlinear system, two distinct solutions branches S1 and S2 intersect. A popular method of branch switching from S1 to S2 at x0 is to use an orthogonal vector to the tangent vector to S1at x0 as an initial guess for the tangent vector to S2 at x0. We describe an improved version of this method using a bisection-like procedure, which is especially useful for large problems.