An Adaptation of Krylov Subspace Methods to Path Following Problems

A procedure is outlined for adapting Krylov subspace methods to solving approximately the underdetermined linear systems that arise in path following (continuation, homotopy) methods. This procedure, in addition to preserving the usual desirable features of Krylov subspace methods, has the advantages of satisfying orthogonality constraints exactly and of not introducing ill-conditioning through poor scaling.