Every Newton step in an interior-point method for optimization requires a solution of a symmetric indefinite system of linear equations. Most of today’s codes apply direct solution methods to perform this task. The use of logarithmic barriers in interior point methods causes unavoidable ill-conditioning of linear systems and, hence, iterative methods fail to provide sufficient accuracy unless a...

The problem of recovering a parameter function based on measurements of solutions of a system of partial diierential equations in several space variables leads to a number of computational challenges. Upon discretization of a regularized formulation a large, sparse constrained optimization problem is obtained. Typically in the literature , the constraints are eliminated and the resulting uncons...

Image restoration is often solved by minimizing an energy function consisting of a datafidelity term and a regularization term. A regularized convex term can usually preserve the image edges well in the restored image. In this paper, we consider a class of convex and edgepreserving regularization functions, i.e., multiplicative half-quadratic regularizations, and we Supported by The National Ba...

The application of nonlinear schemes like dual time stepping as preconditioners in matrix-free Newton– Krylov-solvers is considered and analyzed, with a special emphasis on unsteady viscous flows. We provide a novel formulation of the left preconditioned operator that says it is in fact linear in the matrix-free sense, but changes the Newton scheme. This allows to get some insight in the conver...

A new class of hybrid schemes and composite inner-outer iterative schemes in conjunction with Picard and Newton methods based on explicit approximate inverse arrowtype matrix techniques is introduced. Isomorphic methods in conjunction with explicit preconditioned schemes based on approximate inverse matrix techniques are presented for the efficient solution of arrow-type linear systems. Applica...

The application of nonlinear schemes like dual time stepping as preconditioners in matrix-free Newton-Krylov-solvers is considered and analyzed. We provide a novel formulation of the left preconditioned operator that says it is in fact linear in the matrix-free sense, but changes the Newton scheme. This allows to get some insight in the convergence properties of these schemes which are demonstr...

In this paper we analyze a class of approximate constraint preconditioners in the acceleration of Krylov subspace methods fot the solution of reduced Newton systems arising in optimization with interior point methods. We propose a dynamic sparsification of the Jacobian matrix at every stage of the interior point method. Spectral analysis of the preconditioned matrix is performed and bounds on i...

To find an optimum accelerating parameter of the SOR method is important and a difficult part of the problem. It is more difficult to estimate many optimum parameters of the GSOR method. In this talk, we propose a new algorithm to estimate the optimum parameters of the GSOR method. The key point to estimate these parameters is using a preconditioned matrix constructed by a part of the coefficie...

A list of technical reports, including some abstracts and copies of some full reports may be found at: A fast vectorised implementation of Wallace's normal random number generator. April 1997. Abstract Preconditioned conjugate gradient method is applied for solving linear systems Ax = b where the matrix A is the discretization matrix of second-order elliptic operators. In this paper, we conside...

A major problem in obtaining an efficient implementation of fully implicit RungeKutta (IRK) methods applied to systems of differential equations is to solve the underlying systems of nonlinear equations. Their solution is usually obtained by application of modified Newton iterations with an approximate Jacobian matrix. The systems of linear equations of the modified Newton method can actually b...