Benner, Peter; Mach, Thomas(Computing (Vienna/New York), 2010-06-09)
The hierarchical ( backslashfancyscriptH -) matrix format allows storing a variety of dense matrices from certain applications in a special data-sparse way with linear-polylogarithmic complexity. Many operations from linear ...
Bonet, José; Wegner, Sven Ake(Functiones et Approximatio, Commentarii Mathematici, 2011)
We establish a criterion to decide when a countable projective limit of countable inductive limits of normed spaces is bornological. We compare the conditions occurring within our criterion with well-known abstract conditions ...
Mach, Thomas; Vandebril, Raf(SIAM Journal on Matrix Analysis and Applications, 2014)
In this paper we discuss the deflation criterion used in the extended QR algorithm based on the chasing of rotations. We provide absolute and relative perturbation bounds for this deflation criterion. Further, we present ...
Mach, Thomas; Van Barel, Marc; Vandebril, Raf(Journal of Computational and Applied Mathematics, 2014-12-15)
In inverse eigenvalue problems one tries to reconstruct a matrix, satisfying some constraints, given some spectral information. Here, two inverse eigenvalue problems are solved. First, given the eigenvalues and the first ...
Mach, Thomas; Pranić, Miroslav S.; Vandebril, Raf(Electronic Transactions on Numerical Analysis, 2014)
It has been shown that approximate extended Krylov subspaces can be computed, under certain assumptions, without any explicit inversion or system solves. Instead, the vectors spanning the extended Krylov space are retrieved ...
Aurentz, Jared L.; Mach, Thomas; Vandebril, Raf; Watkins, David S.(Electronic Transactions on Numerical Analysis, 2015)
A fast Fortran implementation of a variant of Gragg's unitary Hessenberg QR algorithm is presented. It is proved, moreover, that all QR- And QZ-like algorithms for the unitary eigenvalue problems are equivalent. The algorithm ...
Aurentz, Jared L.; Mach, Thomas; Vandebril, Raf; Watkins, David S.(SIAM Journal on Matrix Analysis and Applications, 2015)
A stable algorithm to compute the roots of polynomials is presented. The roots are found by computing the eigenvalues of the associated companion matrix by Francis's implicitly shifted QR algorithm. A companion matrix is ...
Benner, Peter; Börm, Steffen; Mach, Thomas; Reimer, Knut(Computing and Visualization in Science, 2015-03-04)
The computation of eigenvalues of large-scale matrices arising from finite element discretizations has gained significant interest in the last decade (Knyazev et al. in Numerical solution of PDE eigenvalue problems, vol ...
Farkas, Bálint; Wegner, Sven Ake(American Mathematical Monthly, 2016-10-01)
It is not hard to prove that a uniformly continuous real function, whose integral up to infinity exists, vanishes at infinity, and it is probably little known that this statement runs under the name "Barbalat's lemma." In ...
Tahir, M. H.; Cordeiro, Gauss M.; Alzaatreh, Ayman; Mansoor, M.; Zubair, M.(Communications in Statistics - Theory and Methods, 2016-12-16)
The logistic distribution has a prominent role in the theory and practice of statistics. We introduce a new family of continuous distributions generated from a logistic random variable called the logistic-X family. Its ...
Alzaatreh, Ayman; Mansoory, M.; Tahirz, M. H.; Zubair, M.; Ghazalik, Shakir Ali(Hacettepe Journal of Mathematics and Statistics, 2016)
A new distribution, namely, the Gamma-Half-Cauchy distribution is proposed. Various properties of the Gamma-Half-Cauchy distribution are studied in detail such as limiting behavior, moments, mean deviations and Shannon ...
Aurentz, Jared L.; Mach, Thomas; Robol, Leonardo; Vandebril, Raf; Watkins, David S.(arXiv, 2016-11-08)
Two generalizations of the companion QR algorithm by J.L. Aurentz, T. Mach, R. Vandebril, and D.S. Watkins, SIAM Journal on Matrix Analysis and Applications, 36(3): 942--973, 2015, to compute the roots of a polynomial are ...
Kussainov, A. S.; Pya, N.(Journal of Physics: Conference Series, 2016-09-05)
We have assessed the potential applications of the neutron monitor hardware as random number generator for normal and uniform distributions. The data tables from the acquisition channels with no extreme changes in the ...
In the last decade matrix polynomials have been investigated with the primary focus on adequate linearizations and good scaling techniques for computing their eigenvalues. In this article we propose a new backward stable ...
Jagels, Carl; Mach, Thomas; Reichel, Lothar; Vandebril, Raf(Linear Algebra and Its Applications, 2016-12-01)
This article deduces geometric convergence rates for approximating matrix functions via inverse-free rational Krylov methods. In applications one frequently encounters matrix functions such as the matrix exponential or ...
A unitary symplectic similarity transformation for a special class of Hamiltonian matrices to extended Hamiltonian Hessenberg form is presented. Whereas the classical Hessenberg form links to Krylov subspaces, the extended ...
Tahir, M. H.; Cordeiro, Gauss M.; Alzaatreh, Ayman; Mansoor, M.; Zubair, M.(Communications in Statistics: Simulation and Computation, 2016-11-25)
Many distributions have been used as lifetime models. In this article, we propose a new three-parameter Weibull–Pareto distribution, which can produce the most important hazard rate shapes, namely, constant, increasing, ...
Mach, Thomas; Reichel, Lothar; Van Barel, Marc; Vandebril, R.(Journal of Computational and Applied Mathematics, 2016-09-01)
Integral equations of the first kind with a smooth kernel and perturbed right-hand side, which represents available contaminated data, arise in many applications. Discretization gives rise to linear systems of equations ...
Wei, Dongming; Zhang, Zhenbu(Electronic journal of differential equations, 2001)
In this work, we compare a parabolic equation with an elliptic
equation both of which are used in modeling temperature profile of a powerlaw
polymer
ow in a semi-infinite straight pipe with circular cross section.
We ...
Lefton, Lew; Wei, Dongming(Electronic journal of differential equations, 2001)
We study approximations of the steady state Stokes problem governed
by the power-law model for viscous incompressible non-Newtonian flow
using the penalty formulation. We establish convergence and find error estimates.