Iterative methods for large continuation problems

Iterative Methods for Large Continuation Problems

The computation of solution paths for continuation problems requires the solution of a sequence of nonlinear systems of equations. Each nonlinear system can be solved by computing the solution of a succession of linear systems of equations determined by Jacobian matrices associated with the nonlinear system of equations. Points on the solution path where the Jacobian matrix is singular are refe...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

Iterative Solution Methods for Large Linear Discrete Ill-posed Problems

This paper discusses iterative methods for the solution of very large severely ill-conditioned linear systems of equations that arise from the discretization of linear ill-posed problems. The right-hand side vector represents the given data and is assumed to be contaminated by errors. Solution methods proposed in the literature employ some form of ltering to reduce the in uence of the error in ...

Iterative Projection Methods for Large–scale Nonlinear Eigenvalue Problems

In this presentation we review iterative projection methods for sparse nonlinear eigenvalue problems which have proven to be very efficient. Here the eigenvalue problem is projected to a subspace V of small dimension which yields approximate eigenpairs. If an error tolerance is not met then the search space V is expanded in an iterative way with the aim that some of the eigenvalues of the reduc...

Homotopy Continuation Methods for Nonlinear Complementarity Problems

A complementarity problem with a continuous mapping f from R n into itself can be written as the system of equations F(x, y ) = 0 and ( x , y ) > 0. Here F is the mapping from R ~ " into itself defined by F(x, y) = ( x l y ,, x 2 y Z , . . . , x , ~ y e , y f f x ) ) . Under the assumption that the mapping f is a P,,-function, we study various aspects of homotopy continuation methods that trace...