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We discuss discrete‐time dynamical systems depending on a parameter μ. Assuming that the system matrix A(μ)$A(\mu)$ is given, but the parameter μ is unknown, we infer the most‐likely parameter μm≈μ$\mu _{m}\approx \mu$ from an observed trajectory x of the dynamical system. We use parametric eigenpairs (vi(μ),λi(μ))$(v_{i}(\mu),\lambda _{i}(\mu))$ of the system matrix A(μ)$A(\mu)$ computed with Newton's method based on a Chebyshev expansion. We then represent x in the eigenvector basis defined by the vi(μ)$v_{i}(\mu)$ and compare the decay of the components with predictions based on the λi(μ)$\lambda _{i}(\mu)$. The resulting estimates for μ are combined using a kernel density estimator to find the most likely value for μm$\mu _{m}$ and a corresponding uncertainty quantification. [ABSTRACT FROM AUTHOR]

Linear ill‐posed problems often are analyzed in function spaces using tools from functional analysis, while their numerical solution typically is computed by first discretizing the problem and then applying tools from finite‐dimensional linear algebra. The Chebfun package makes it possible to solve linear ill‐posed problems without explicit discretization. This work discusses the use of Tikhonov regularization with a fairly general linear regularization operator within the Chebfun framework. [ABSTRACT FROM AUTHOR]

SUMMARY The preconditioned inverse iteration is an efficient method to compute the smallest eigenpair of a symmetric positive definite matrix M. Here we use this method to find the smallest eigenvalues of a hierarchical matrix. The storage complexity of the data-sparse [ABSTRACT FROM AUTHOR]

We show that extended Hamiltonian Hessenberg matrices arise naturally in projection-based model order reduction. Therefore we reduce a large dynamical system by projecting it on an extended Krylov subspace. The eigenvalues of the reduced order model can then be computed directly by applying the extended Hamiltonian QR algorithm. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

We present a numerical example illustrating that the deflation procedure in Francis's implicitly shifted QR algorithm can be improved by a deflation criteria based on the QR decomposition of the upper Hessenberg matrix. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

In [1] we presented an extension of the alternating direction implicit (ADI) method for the solution of Lyapunov equations [ABSTRACT FROM AUTHOR]