### Pseudo-arclength continuation

One option for choosing is to select a hyperplane passing through that is orthogonal to the vector :

| (3)

So, the Newton iteration becomes:

| (4)

| (5)

Then one can prove that the Newton iteration for (2) will converge to a point on the curve from provided that the stepsize is sufficiently small and that the curve is regular (rank ). Having found the new point on the curve we need to compute the tangent vector at that point:

| (6)

Furthermore the direction along the curve must be preserved: , so we get the ()-dimensional appended system

| (7)

Upon solving this system, must be normalized.