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Branch Point Locator

The location of BPC points in the non-generic situation (i.e. where some symmetry is present) as zeros of the test functions is numerically suspect because no local quadratic convergence can be guaranteed. This difficulty can be avoided by introducing an additional unknown and considering the minimally extended system:

|  |  | (50)

where is defined as in (84) and is the bordering vector in (86). We solve this system with respect to and by Newton's method with initial . A branch point corresponds to a regular solution of system (50) (see [3],p. 165). We note, however that the second order partial derivatives (Hessian) of with respect to and are required. The tangent vector at the BPC singularity is approximated as where is the tangent vector in the continuation point previous to the BPC and is the one in the next point.