Bifurcation detection with the (un)preconditioned GMRES(m) Original Research Article

When iterative solvers are used for the solution of the linearized equations sets arising from Newtonʹs method, detection of bifurcation points in the solution space can be done by solving several eigenvalue problems with the Jacobian matrix during parameter continuation. Monitoring the condition number of appropriate matrices involved in the GMRES method employed here, replaces or significantly reduces the costly eigenvalue computations. The effectiveness of the detection method is examined in connection with the usage of unpre- and preconditioned iterative solvers.