AbstractThe two‐root (i,j,k) generalized Padé approximation (GPA) and three‐root (i,j,k,l) GPA as well as the two‐root continued fraction approximation (CFA) and the three‐root CFA are applied to the model of a three‐state avoided crossing. These two procedures for analytic continuation are compared. The results indicate that both methods provide good continuation into the complex plane and can be applied to locate the complex branch point. When the same input data are chosen, the GPA works slightly better than the CFA. According to our analysis, the two‐root procedure can be applied to locate the branch point around each region of avoided crossing in the problem of a multi‐state avoided crossing. The accuracy of the result is found to be associated the location of comple