A priori error bounds on invariant subspace approximations by block Krylov subspaces

On Krylov Subspace Approximations to Thematrix Exponential

Convergence of Restarted Krylov Subspaces to Invariant Subspaces

The performance of Krylov subspace eigenvalue algorithms for large matrices can be measured by the angle between a desired invariant subspace and the Krylov subspace. We develop general bounds for this convergence that include the effects of polynomial restarting and impose no restrictions concerning the diagonalizability of the matrix or its degree of nonnormality. Associated with a desired se...

Enhancement of Krylov Subspace Spectral Methods by Block Lanczos Iteration

Abstract. This paper presents a modification of Krylov subspace spectral (KSS) methods, which build on the work of Golub, Meurant and others, pertaining to moments and Gaussian quadrature to produce high-order accurate approximate solutions to variable-coefficient time-dependent PDEs. Whereas KSS methods currently use Lanczos iteration to compute the needed quadrature rules, our modification us...

Roundoff Error Analysis of Algorithms Based on Krylov Subspace Methods

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 ...

Rational invariant subspace approximations with applications

Subspace methods such as MUSIC, Minimum Norm, and ESPRIT have gained considerable attention due to their superior performance in sinusoidal and direction-of-arrival (DOA) estimation, but they are also known to be of high computational cost. In this paper, new fast algorithms for approximating signal and noise subspaces and that do not require exact eigendecomposition are presented. These algori...