Počet záznamů: 1

On Chebyshev Polynomials of Matrices

  1. 1.
    0346245 - UIVT-O 2011 RIV US eng J - Článek v odborném periodiku
    Faber, V. - Liesen, J. - Tichý, Petr
    On Chebyshev Polynomials of Matrices.
    SIAM Journal on Matrix Analysis and Applications. Roč. 31, č. 4 (2010), s. 2205-2221 ISSN 0895-4798
    Grant CEP: GA AV ČR IAA100300802
    Grant ostatní: GA AV ČR(CZ) M100300901
    Výzkumný záměr: CEZ:AV0Z10300504
    Zdroj financování: I - institucionální podpora na rozvoj VO
    Klíčová slova: matrix approximation problems * Chebyshev polynomials * complex approximation theory * Krylov subspace methods * Arnoldi's method
    Kód oboru RIV: BA - Obecná matematika
    Impakt faktor: 1.725, rok: 2010

    The mth Chebyshev polynomial of a square matrix A is the monic polynomial that minimizes the matrix 2-norm of p(A) over all monic polynomials p(z) of degree m. This polynomial is uniquely defined if m is less than the degree of the minimal polynomial of A. We study general properties of Chebyshev polynomials of matrices, which in some cases turn out to be generalizations of well-known properties of Chebyshev polynomials of compact sets in the complex plane. We also derive explicit formulas of the Chebyshev polynomials of certain classes of matrices, and explore the relation between Chebyshev polynomials of one of these matrix classes and Chebyshev polynomials of lemniscatic regions in the complex plane.
    Trvalý link: http://hdl.handle.net/11104/0187315
    Název souboruStaženoVelikostKomentářVerzePřístup
    0346245.pdf0801.6 KBAutorský preprintpovolen