Group Homotopy algorithm with a parameterized Newton iteration for symmetric eigen problems

Abstract

In this paper we develop a general Homotopy method called the Group Homotopy method to solve the symmetric eigenproblem. The Group Homotopy method overcomes notable drawbacks of the existing Homotopy method, namely, (i) the possibility of breakdown or having a slow rate of convergence in the presence of clustering of the eigenvalues and (ii) the absence of any definite criterion to choose a step size that guarantees the convergence of the method. On the other hand, the Group Homotopy method maintains attractive features of the ordinary Homotopy method such as the natural parallelism and the structure preserving properties. © Springer-Verlag Berlin Heidelberg 2005.