This paper proposes two new algorithms for the direction of arrival (DOA) estimation of P radiating sources. Unlike the classical subspace-based methods, they do not resort to the eigen-decomposition of the covariance matrix of the received data. Indeed, the proposed algorithms involve the building of the signal subspace from the Krylov subspace of order P associated with the covariance matrix ...

We present a novel method to compute the overlap Dirac operator at zero and nonzero quark chemical potential. To approximate the sign function of large, sparse matrices, standard methods project the operator on a much smaller Krylov subspace, on which the matrix function is computed exactly. However, for large lattices this subspace can still be too large for an efficient calculation of the sig...

Two Krylov subspace iterative methods, GMRES and QMR, were studied in conjunction with several preconditioning techniques for solving the linear system raised from the finite element discretisation of incompressible Navier-Stokes equations for hydrodynamic problems. The preconditioning methods under investigation were the incomplete factorisation methods such as ILU(0) and MILU, the Stokes prec...

It is shown that the four vector extrapolation methods, minimal polynomial extrapolation, reduced rank extrapolation, modified minimal polynomial extrapolation, and topological epsilon algorithm, when applied to linearly generated vector sequences, are Krylov subspace methods, and are equivalent to some well known conjugate gradient type methods. A unified recursive method that includes the con...

We compare two approaches to compute a fraction of the spectrum of dense symmetric definite generalized eigenproblems: one is based on the reduction to tridiagonal form, and the other on the Krylov-subspace iteration. Two large-scale applications, arising in molecular dynamics and material science, are employed to investigate the contributions of the application, architecture, and parallelism o...

The purpose of this work is to compare the performance of some preconditioned iterative methods for solving the linear systems of equations, formed at each time-integration step of two-dimensional incompressible NavierStokes equations of fluid flow. The Navier-Stokes equations are discretized in an implicit and upwind control volume formulation. The iterative methods used in this paper include ...

The discretization of second-order elliptic stochastic partial differential equations in primal or mixed formulation, where the diffusion coefficient is modelled via a truncated Karhunen-Loève expansion, results in a sequence of linear systems. We employ Krylov subspace recycling methods which utilize information generated during the solution of a previous system in order to improve the converg...

This paper presents an investigation into fault tolerance for the fine-grained parallel algorithm for computing an incomplete LU factorization. Results concerning the convergence of the algorithm with respect to the occurrence of faults, and the impact of any sub-optimality in the produced incomplete factors in Krylov subspace solvers are given. Numerical tests show that the simple algorithmic ...

Krylov subspace methods have been applied successfully to solve various problems in Numerical Linear Algebra. The Netherlands have been a pioneer country in the development of Krylov methods over the past years. Methods like the Conjugate Gradient Squared (CGS), Bi-Conjugate Gradient Stabilized (BiCGSTAB), Nested GMRES (GMRESR), and the Induced Dimension Reduction method (IDR) are examples of K...