One of the possible ways of solving general problems of constrained nonlinear optimization is to convert them into a sequence of unconstrained problems. Then the need arises to solve an unconstrained optimization problem reliably and efficiently. For this aim, Newton methods are usually applied, often in combination with sparse Cholesky decomposition. In practice, however, this approach may not...

Alternating methods for image deblurring and denoising have recently received considerable attention. The simplest of these methods are two-way methods that restore contaminated images by alternating between deblurring and denoising. This paper describes Krylov subspace-based two-way alternating iterative methods that allow the application of regularization operators different from the identity...

Systems AVRAM SIDI Computer Science Department Technion Israel Institute of Technology Haifa 32000 ISRAEL E-mail: [email protected] http://www.cs.technion.ac.il/ ̃asidi/ Abstract: We consider the solution by Krylov subspace methods of a certain class of hermitian indefinite linear systems, such as those that arise from discretization of the Stokes equations in incompressible fluid mechanic...

Communication-Avoiding Krylov Subspace Methods in Theory and Practice

Transport equations have many important applications. Because the equations are based on highly non-normal operators, they present diiculties in numerical computations. The iterative methods have been shown to be one of eecient numerical methods to solve transport equations. However, because of the nature of transport problems, convergence of iterative methods tends to slow for many important p...

Krylov subspace spectral methods have been shown to be high-order accurate in time and more stable than explicit time-stepping methods, but also more difficult to implement efficiently. This paper describes how these methods can be fashioned into practical solvers by exploiting the simple structure of differential operators Numerical results concerning accuracy and efficiency are presented for ...

This paper reviews the main properties, and most recent developments, of Krylov subspace spectral (KSS) methods for time-dependent variable-coefficient PDE. These methods use techniques developed by Golub and Meurant for approximating elements of functions of matrices by Gaussian quadrature in the spectral domain in order to achieve high-order accuracy in time and stability characteristic of im...

There is a class of linear problems for which the computation of the matrix-vector product is very expensive since a time consuming approximation method is necessary to compute it with some prescribed relative precision. In this paper we investigate the effect of an approximately computed matrix-vector product on the convergence and accuracy of several Krylov subspace solvers. The obtained insi...

This thesis deals with linear ill-posed problems related to compact operators, and iterative Krylov subspace methods for solving discretized versions of these. Linear compact operators in infinite dimensional Hilbert spaces will be investigated and several results on the singular values and eigenvalues for such will be presented. A large subset of linear compact operators consists of integral o...

We present a general framework for a number of techniques based on projection methods onàugmented Krylov subspaces'. These methods include the deeated GM-RES algorithm, an inner-outer FGMRES iteration algorithm, and the class of block Krylov methods. Augmented Krylov subspace methods often show a signiicant improvement in convergence rate when compared with their standard counterparts using the...