The inherent uncertainties in geometry, material properties, etc. of engineering structures can be represented by stochastic models, where the parameters are described by probabilistic laws. Results from any analysis based on stochastic models inherit probabilistic information as well, which can be used e.g. for reliability analysis. Particularly in linear dynamics of structures the calculation...

The subspace iteration method (SIM) is a numerical procedure for normal mode analysis which has shown to be robust and reliable for solving very large general eigenvalue problems. Although its classical form as introduced by Bathe in the seventies of the last century is less efficient than the Lanczos iteration method in terms of CPU time, it is beneficial in terms of storage use if a very larg...

A novel formulation of approximate truncated balanced realization (TBR) is introduced to unify three approaches: two iterative methods for solving the underlying Lyapunov equations – the alternating directions implicit (ADI) iteration and the rational Krylov subspace method (RKSM) – and a two-step procedure that performs a Krylov-based projection and subsequently direct TBR. The framework allow...

The A-gradient minimization of the Rayleigh quotient allows to construct robust and fastconvergent eigensolvers for the generalized eigenvalue problem for (A,M) with symmetric and positive definite matrices. The A-gradient steepest descent iteration is the simplest case of more general restarted Krylov subspace iterations for the special case that all step-wise generated Krylov subspaces are tw...

The inherent uncertainties in geometry, material properties, etc. of engineering structures can be represented by stochastic models, where the parameters are described by probabilistic laws. Results from any analysis based on stochastic models inherit probabilistic information as well, which can be used e.g. for reliability analysis. Particularly in linear dynamics of structures the calculation...

We consider and analyze applying a spectral inverse iteration algorithm and its subspace iteration variant for computing eigenpairs of an elliptic operator with random coefficients. With these iterative algorithms the solution is sought from a finite dimensional space formed as the tensor product of the approximation space for the underlying stochastic function space, and the approximation spac...

In this paper, we present a new algorithm for tracking the generalized signal subspace recursively. It is based on an interpretation of the generalized signal subspace as the solution of a constrained minimization task. This algorithm, referred to as the CGST algorithm, guarantees the Cx-orthonormality of the estimated generalized signal subspace basis at each iteration which Cx denotes the cor...

We consider sequential, i.e., Gauss-Seidel type, subspace correction methods for the iterative solution of symmetric positive definite variational problems, where the order of subspace correction steps is not deterministically fixed as in standard multiplicative Schwarz methods. Here, we greedily choose the subspace with the largest (or at least a relatively large) residual norm for the next up...

In this paper, a three-dimensional subspace method is proposed, in which the search direction generated by minimizing approximation model of objective function subspace. The not unique, and alternatives can be chosen between symmetric quadratic conic specific criteria. Moreover, idea WLY conjugate gradient applied to characterize change adjacent iteration points. strategy initial stepsize nonmo...

The approximate solutions in standard iteration methods for linear systems Ax = b, with A an n by n nonsingular matrix, form a subspace. In this subspace, one may try to construct better approximations for the solution x. This is the idea behind Krylov subspace methods. It has led to very powerful and e$cient methods such as conjugate gradients, GMRES, and Bi-CGSTAB. We will give an overview of...