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 b Î R and
considering the minimally extended system:
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where G is defined as in (86) and [p1T p2T p3]T is the bordering vector [w01;w02;w03]T in (88). We solve this system with respect to x,T,a and b by Newton's method with initial b = 0. A branching point (x,T,a) corresponds to a regular solution (x,T,a,0) of system (53) (see [2],p. 165). We note, however that the second order partial derivatives (Hessian) of f with respect to x and a are required. The tangent vector v1st at the BPC singularity is approximated as v1st=[(v1+v2)/2] where v1 is the tangent vector in the continuation point previous to the BPC and v2 is the one in the next point.