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Mathematics: Recent submissions

  • A note on the convexity of the Moore–Penrose inverse 
    Nordström, Kenneth (Linear Algebra and its Applications, 2018-02-01)
    Abstract This note is a sequel to an earlier study (Nordström [7]) on convexity properties of the inverse and Moore–Penrose inverse, in which the following question was raised. Given nonnegative definite matrices A and B ...
  • The heart of the Banach spaces 
    Wegner, Sven-Ake (Journal of Pure and Applied Algebra, 2017-11-01)
    Abstract Consider an exact category in the sense of Quillen. Assume that in this category every morphism has a kernel and that every kernel is an inflation. In their seminal 1982 paper, Beĭlinson, Bernstein and Deligne ...
  • On K-means algorithm with the use of Mahalanobis distances 
    Melnykov, Igor; Melnykov, Volodymyr (Statistics & Probability Letters, 2014-01-01)
    Abstract The K-means algorithm is commonly used with the Euclidean metric. While the use of Mahalanobis distances seems to be a straightforward extension of the algorithm, the initial estimation of covariance matrices can ...
  • Controllable asymmetric phase-locked states of the fundamental active photonic dimer 
    Kominis, Yannis; Kovanis, Vassilios; Bountis, Tassos (Physical Review, 2017-10-16)
    Coupled semiconductor lasers are systems possessing complex dynamics that are interesting for numerous applications in photonics. In this work, we investigate the existence and the stability of asymmetric phase-locked ...
  • Stability Through Asymmetry: Modulationally Stable Nonlinear Supermodes of Asymmetric non-Hermitian Optical Couplers 
    Kominis, Yannis; Bountis, Tassos; Flach, Sergej (ArXiv, 2017-06-23)
    We analyze the stability of a non-Hermitian coupler with respect to modulational inhomogeneous perturbations in the presence of unbalanced gain and loss. At the parity-time (PT) symmetry point the coupler is unstable. ...
  • Spectral Signatures of Exceptional Points and Bifurcations in the Fundamental Active Photonic Dimer 
    Kominis, Yannis; Kovanis, Vassilios; Bountis, Tassos (ArXiv, 2017-10-04)
    The fundamental active photonic dimer consisting of two coupled quantum well lasers is inves-tigated in the context of the rate equation model. Spectral transition properties and exceptional points are shown to occur under ...
  • Nonlinear Waves in Rods and Beams of Power-Law Materials 
    Wei, Dongming; Skrzypacz, Piotr; Yu, Xijun (Journal of Applied Mathematics, 2017-07-13)
    Some novel traveling waves and special solutions to the 1D nonlinear dynamic equations of rod and beam of power-law materials are found in closed forms. The traveling solutions represent waves of high elevation that ...
  • Periodic solutions of a graphene based model in micro-electro-mechanical pull-in device 
    Wei, D.; Kadyrov, S.; Kazbek, Z. (Applied and Computational Mechanics, 2017)
    Phase plane analysis of the nonlinear spring-mass equation arising in modeling vibrations of a lumped mass attached to a graphene sheet with a fixed end is presented. The nonlinear lumped-mass model takes into account the ...
  • The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport 
    Kominis, Yannis; Bountis, Tassos; Flach, Sergej (Scientific Reports, 2016-09-19)
    We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, ...
  • On the QR decomposition of backslashfancyscript H -matrices 
    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 ...
  • Bornological projective limits of inductive limits of normed spaces 
    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 ...
  • On deflations in extended QR algorithms 
    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 ...
  • Inverse eigenvalue problems for extended Hessenberg and extended tridiagonal matrices 
    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 ...
  • Computing approximate (block) rational Krylov subspaces without explicit inversion with extensions to symmetric matrices 
    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 ...
  • Fast and stable unitary QR algorithm 
    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 ...
  • Fast and backward stable computation of roots of polynomials 
    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 ...
  • Computing the eigenvalues of symmetric H2-matrices by slicing the spectrum 
    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 ...
  • The logistic-X family of distributions and its applications 
    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 ...
  • The gamma half-Cauchy distribution: Properties and applications 
    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 ...
  • Roots of Polynomials: on twisted QR methods for companion matrices and pencils 
    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 ...