A structure-preserving dimension reduction algorithm for large-scale second-order dynamical systems is presented. It is a projection method based on a second-order Krylov subspace. A second-order Arnoldi (SOAR) method is used to generate an orthonormal basis of the projection subspace. The reduced system not only preserves the second-order structure but also has the same order of approximation ...

Krylov-subspace methods, such as the multistage Wiener filter and conjugate gradient method, are often used for reduced-dimension adaptive beamforming. These techniques do not, however, allow for steering vector mismatch, which is typically present in many applications of interest, including passive sonar. Here, we discuss recently proposed robust methods that do allow for steering vector misma...

Abstract. The need to evaluate expressions of the form f(A)v, where A is a large sparse or structured symmetric matrix, v is a vector, and f is a nonlinear function, arises in many applications. The extended Krylov subspace method can be an attractive scheme for computing approximations of such expressions. This method projects the approximation problem onto an extended Krylov subspace K(A) = s...

This article is devoted to the numerical solution of large-scale quadratic eigenvalue problems. Such problems arise in a wide variety of applications, such as the dynamic analysis of structural mechanical systems, acoustic systems, fluid mechanics, and signal processing. We first introduce a generalized second-order Krylov subspace based on a pair of square matrices and two initial vectors and ...

Means of applying Krylov subspace techniques for adaptively extracting accurate reducedorder models of large-scale nonlinear dynamical systems is a relatively open problem. There has been much current interest in developing such techniques. We focus on a bi-linearization method, which extends Krylov subspace techniques for linear systems. In this approach, the nonlinear system is first approxim...

For nonselfadjoint elliptic boundary value problem which are preconditioned by a sub-structuring method, i.e., nonoverlapping domain decomposition, we introduce and study the concept of subspace orthogonalization. In subspace orthogonalization variants of Krylov methods the computation of inner products and vector updates, and the storage of basis elements is restricted to a (presumably small) ...

Optimal Krylov subspace methods like GMRES and GCR have to compute an orthogonal basis for the entire Krylov subspace to compute the minimal residual approximation to the solution. Therefore, when the number of iterations becomes large, the amount of work and the storage requirements become excessive. In practice one has to limit the resources. The most obvious ways to do this are to restart GM...

We conduct an experimental study on the behavior of several preconditioned iterative methods to solve nonsymmetric matrices arising from computational ̄uid dynamics (CFD) applications. The preconditioned iterative methods consist of Krylov subspace accelerators and a powerful general purpose multilevel block ILU (BILUM) preconditioner. The BILUM preconditioner and an enhanced version of it are ...

The cubed-sphere grid of gnomonic type [ 7, 8] is used in this study. The grid is generated by mapping the six faces of an inscribed cube to the sphere surface using gnomonic projection. The six expanded patches are continuously attached together with proper boundary conditions. On each patch, the expressions of the SWEs in local curvilinear coordinates (x, y) ∈ [−π/4, π/4] are identical. When ...