A New Algorithm for Numerical Path Following Applied to an Example from Hydrodynamical Flow
Jacques Huitfeldt, Axel Ruhe · SIAM Journal on Scientific and Statistical Computing · 1990
A numerical algorithm for following a path of solutions to a nonlinear eigenvalue problem is described. It is an Euler–Newton continuation method, where the linear systems are solved with an Arnoldi iteration, where a factorization of the Jacobian matrix at an earlier point is used as a preconditioner.It is shown how the eigenvalues of the Hessenberg matrix produced in the Arnoldi iteration can be used to localize singular points, i.e., turning points or bifurcations along the path. A case of the Taylor problem from hydrodynamics is reported as a numerical example.