The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A cent...

The use of preconditioned Krylov methods is in many applications mandatory for computing efficiently the solution of large sparse nonlinear systems of equations. However, the available preconditioners are often sub-optimal, due to the changing nature of the linearized operator. In this work we introduce and analyze an adaptive preconditioning technique based on the Krylov subspace information g...

We study how the Newton-GMRES iteration can enable dynamic simulators (time-steppers) to perform fixed-point and path-following computations. For a class of dissipative problems, whose dynamics are characterized by a slow manifold, the Jacobian matrices in such computations are compact perturbations of the identity. We examine the number of GMRES iterations required for each nonlinear iteration...

A method for computing band structures for three-dimensional photonic crystals is described. The method combines a mixed finite element discretization on a uniform grid with a fast Fourier transform preconditioner and a preconditioned subspace iteration algorithm. Numerical examples illustrating the behavior of the method are presented.

An algorithm of successive location of the solution is developed for the problem of finding the projection of a point onto the canonical simplex in the Euclidean space R ~. This algorithm converges in a finite number of steps. Each iteration consists in finding the projection of a point onto an affine subspace and requires only explicit and very simple computations.

We interprete non-overlapping domain decomposition methods as multiplicative subspace correction algorithms in the framework of Xu [8]. This allows us to estimate the effects of the perturbation which is created by an inexact solution of the problems on the subdomains that must be solved in each iteration. The general results are applied to finite element discretizations of the Poisson and Stok...

In this paper, the problem of time-varying channel estimation for ZP-OFDM wireless communication systems is considered. Based on Rayleigh Quotient Iteration method, a new adaptive blind subspace channel estimation algorithm is proposed for ZP-OFDM systems. Because SVD is not required, the new algorithm has low complexity. The performance of new method has been validated through extensive simula...

We study the convergence of the Mann Iteration applied to the partial complement of a firmly nonexpansive operator with respect to a linear subspace of a Hilbert space. A new concept considered here. A regularized version is also proposed. Furthermore, to motivate this concept, some applications to robust regression procedures and location problems are proposed.

The implicitly restarted Arnoldi method implicitly applies a polynomial lter to the Arnoldi vectors by use of orthogonal transformations. In this paper, an implicit ltering by rational functions is proposed for the rational Krylov method. This ltering is performed in an eecient way. Two applications are considered. The rst one is the ltering of unwanted eigenvalues using exact shifts. This appr...

The Quadratic Arnoldi algorithm is an Arnoldi algorithm for the solution of the quadratic eigenvalue problem, that exploits the structure of the Krylov vectors. This allows us to reduce the memory requirements by about a half. The method is an alternative to the Second Order Arnoldi method (SOAR). In the SOAR method it is not clear how to perform an implicit restart. We discuss various choices ...