Krylov methods and determinants for detecting bifurcations in one parameter dependent partial differential equations
The authors study the computation of the sign of the determinant for a large matrix as a byproduct of the preconditioned generalized minimal residual (GMRES) method when applied to solve the linear systems arising in the discretization of partial differential equations. Numerical experiments are presented where the technique is applied to detect and locate pitchfork and transcritical bifurcation points on a one parameter dependent system. With an appropriate selection of the initial guess in the GMRES method, the technique is shown to detect and accurately locate bifurcation points. The authors have also presented an analysis that helps to explain the good performance observed in practice. A conclusion and some remarks are included at the end of the paper.
scientific article; zbMATH DE number 5081850
scientific article