The approximation of generalized turning points by Krylov subspace methods (Q1338809)

The author considers a class of nonlinear parameter-dependent operator equations. Certain types of singular solutions of such equations, the so- called generalized turning points, are characterized by \textit{A. Griewank} and \textit{G. W. Reddien} [SIAM J. Numer. Anal. 21, 176-185 (1984; Zbl 0536.65031) and Numer. Math. 48, 591-606 (1986; Zbl 0596.65040)] as regular solutions of suitable larger systems. In this paper a numerical approximation of generalized turning points is presented. The approach is based on the use of Krylov subspaces. Applications to boundary value problems are given and the method is illustrated by numerical examples.