We study the roundoff error propagation in an algorithm which computes the orthonormal basis of a Krylov subspace with Householder orthonormal matrices . Moreover, we analyze special implementations of the classical GMRES algorithm, and of the Full Orthogonalization Method . These techniques approximate the solution of a large sparse linear system of equations on a sequence of Krylov subspaces ...

Since the rst papers on asymptotic waveform evaluation (AWE), reduced order models have become standard for improving interconnect simulation ee-ciency, and very recent work has demonstrated that bi-orthogonalization algorithms can be used to robustly generate AWE-style macromodels. In this paper we describe using block Arnoldi-based orthogo-nalization methods to generate reduced order models f...

In an recent paper [1], DeGroat and Roberts developed a re-orthogonalization scheme for stabilizing eigenstructure updating algorithms. In this note, we show that only part of this scheme, namely the re-normalization, is essential for the stability, so that a cheaper scheme –with roughly half as many computations– can perform equally well. EDICS classification : 5.2 5.2.4 Mailing address : Marc...

(a) (b) (c) b b ˆ Figure 1: Geometric interpretation of the orthogonalization procedure using the Fourier transform as a tool. The group is ? = fI; V g, where V performs the exchange of the components of vectors from R 2. (a) Projection of b on the ?-invariant subspaces relative to U 1 and U ?1. (b) Normalization of the two projections. (c) Recombination of the normalized projections yielding t...

Block-GMRES is an iterative method for solving nonsymmetric systems of linear equations with multiple right-hand sides. Restarting may be needed, due to orthogonalization expense or limited storage. We discuss how restarting affects convergence and the role small eigenvalues play. Then a version of restarted block-GMRES that deflates eigenvalues is presented. It is demonstrated that deflation c...