74 citations · 255 across the 21 of their papers we have counts for
24 papers
On the cyclic limiting behavior of the restarted Arnoldi algorithm for real symmetric matrices with restart length
Vance Faber, Jarek Liesen, Jörg Liesen +1
We prove that the restarted Arnoldi algorithm for real symmetric matrices with restart length has a cyclic limiting behavior. In the terminology established in (arXiv:2209.14…
Linear Systems and Eigenvalue Problems: Open Questions from a Simons Workshop
Noah Amsel, Yves Baumann, Paul Beckman +33
This document presents a series of open questions arising in matrix computations, i.e., the numerical solution of linear algebra problems. It is a result of working groups at the w…
Towards understanding CG and GMRES through examples
Erin Carson, Jörg Liesen, Zdeněk Strakoš
When the CG method for solving linear algebraic systems was formulated about 70 years ago by Lanczos, Hestenes, and Stiefel, it was considered an iterative process possessing a mat…
On the Forsythe conjecture
Vance Faber, Jörg Liesen, Petr Tichý
Forsythe formulated a conjecture about the asymptotic behavior of the restarted conjugate gradient method in 1968. We translate several of his results into modern terms, and genera…
Computing the logarithmic capacity of compact sets having (infinitely) many components with the Charge Simulation Method
Jörg Liesen, Mohamed M. S. Nasser, Olivier Sète
We apply the Charge Simulation Method (CSM) in order to compute the logarithmic capacity of compact sets consisting of (infinitely) many "small" components. This application allows…
On non-Hermitian positive (semi)definite linear algebraic systems arising from dissipative Hamiltonian DAEs
Candan Güdücü, Jörg Liesen, Volker Mehrmann +1
We discuss different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization. For eac…
Centrality of nodes in Federated Byzantine Agreement Systems
André Gaul, Jörg Liesen
The federated Byzantine agreement system (FBAS) is a consensus model introduced by Mazières in 2016 where the participating nodes conceptually form a network, with links between th…
Analysis of the multiplicative Schwarz method for matrices with a special block structure
Carlos Echeverría, Jörg Liesen, Petr Tichý
We analyze the convergence of the (algebraic) multiplicative Schwarz method applied to linear algebraic systems with matrices having a special block structure that arises, for exam…
Mathematical Analysis and Algorithms for Federated Byzantine Agreement Systems
André Gaul, Ismail Khoffi, Jörg Liesen +1
We give an introduction to federated Byzantine agreement systems (FBAS) with many examples ranging from small "academic" cases to the current Stellar network. We then analyze the m…
Block diagonal dominance of matrices revisited: bounds for the norms of inverses and eigenvalue inclusion sets
Carlos Echeverría, Jörg Liesen, Reinhard Nabben
We generalize the bounds on the inverses of diagonally dominant matrices obtained in [16] from scalar to block tridiagonal matrices. Our derivations are based on a generalization o…
The maximum number of zeros of revisited
Jörg Liesen, Jan Zur
Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions $f(z) = \frac{p(z)}{q(z)} - \ov…
How constant shifts affect the zeros of certain rational harmonic functions
Jörg Liesen, Jan Zur
We study the effect of constant shifts on the zeros of rational harmomic functions $f(z) = r(z) - \conj{z}$. In particular, we characterize how shifting through the caustics of …
Using separable non-negative matrix factorization techniques for the analysis of time-resolved Raman spectra
Robert Luce, Peter Hildebrandt, Uwe Kuhlmann +1
The key challenge of time-resolved Raman spectroscopy is the identification of the constituent species and the analysis of the kinetics of the underlying reaction network. In this…
Fast and accurate computation of the logarithmic capacity of compact sets
Jörg Liesen, Olivier Sète, Mohamed M. S. Nasser
We present a numerical method for computing the logarithmic capacity of compact subsets of , which are bounded by Jordan curves and have finitely connected complement.…
Numerical computation of the conformal map onto lemniscatic domains
Mohamed M. S. Nasser, Jörg Liesen, Olivier Sète
We present a numerical method for the computation of the conformal map from unbounded multiply-connected domains onto lemniscatic domains. For -times connected domains the me…
Properties and examples of Faber--Walsh polynomials
Olivier Sète, Jörg Liesen
The Faber--Walsh polynomials are a direct generalization of the (classical) Faber polynomials from simply connected sets to sets with several simply connected components. In this p…
A Note on the Maximum Number of Zeros of
Robert Luce, Olivier Sète, Jörg Liesen
An important theorem of Khavinson & Neumann (Proc. Amer. Math. Soc. 134(4), 2006) states that the complex harmonic function , where is a rational function of de…
Creating images by adding masses to gravitational point lenses
Olivier Sète, Robert Luce, Jörg Liesen
A well-studied maximal gravitational point lens construction of S. H. Rhie produces images of a light source using deflector masses. The construction arises from a circu…
Perturbing rational harmonic functions by poles
Olivier Sète, Robert Luce, Jörg Liesen
We study how adding certain poles to rational harmonic functions of the form , with rational and of degree , affects the number of zeros of the result…
Sharp parameter bounds for certain maximal point lenses
Robert Luce, Olivier Sète, Jörg Liesen
Starting from an -point circular gravitational lens having images, Rhie (2003) used a perturbation argument to construct an -point lens producing images. In t…
Max-min and min-max approximation problems for normal matrices revisited
Jörg Liesen, Petr Tichý
We give a new proof for an equality of certain max-min and min-max approximation problems involving normal matrices. The previously published proofs of this equality apply tools fr…
Characterization of worst-case GMRES
Vance Faber, Jörg Liesen, Petr Tichý
Given a matrix and iteration step , we study a best possible attainable upper bound on the GMRES residual norm that does not depend on the initial vector . This quantity…
The field of values bound on ideal GMRES
Jörg Liesen, Petr Tichý
A widely known result of Elman, and its improvements due to Starke, Eiermann and Ernst, gives a bound on the worst-case GMRES residual norm using quantities related to the field of…
A framework for deflated and augmented Krylov subspace methods
André Gaul, Martin H. Gutknecht, Jörg Liesen +1
We consider deflation and augmentation techniques for accelerating the convergence of Krylov subspace methods for the solution of nonsingular linear algebraic systems. Despite some…