Large Scale Problems

Abstract

As has been pointed out occasionally in the previous chapters, one of the primary applications of continuation methods involves the numerical solution of nonlinear eigenvalue problems. Such problems are likely to have arisen from a discretization of an operator equation in a Banach space context, and involving an additional “eigenvalue” parameter. Some examples were touched upon in Chapter 8. As a result of the discretization and the wish to maintain a reasonably low truncation error, the corresponding finite dimensional problem H(u) = 0 where H : R^N+1 → R^N, may require that N be quite large. This then leads to the task of solving large scale continuation problems.